Probability Class 10

Ex 14.1, 1 teachoo
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ =
We know that
P(not E) = 1 — P(E)
P(not E) + P(E) =1
-. Probability of an event E + Probability of the event ‘not E’ = 1.

///'

teachoo

Ex 14.1, 3
Why is tossing a coin considered to be a fair way of deciding which
team should get the ball at the beginning of a football game?

Cy
When we toss a coin, Tails Heads
the possible outcomes are only two, head or tail.
So, either head could come or tail
So, heads and tails are equally likely outcomes.
Therefore, the result of an individual toss is completely unpredictable

teachoo

Ex 14.1, 4
Which of the following cannot be the probability of an event?
(A) = (B)-15 — (c)15% == (D) 0.7

0 < Probability of event E <1
So, probability of an event cannot be negative or greater than 1.
Therefore, -1.5 cannot be a probability of an event.
(B) Is the answer

Ex 14.1, 5 teachoo
If P(E} = 0.05, what is the probability of ‘not E’?
P(Not E) = 1 — P(E)
=1-0.05
=0.95
Therefore, the probability of ‘not E’ is 0.95,

Ex 14.1, 6 (i) (Method 1) teachoo
A bag contains lemon flavoured candies only. Malini takes out one
candy without looking into the bag. What is the probability that
she takes out
(i) an orange flavoured candy?
Let total number of candies = 100
Number of candies which are orange flavoured = 0
P(candy taken out is orange flavoured)

_ Number of candies which are orange flavoured

~ Total number of candies

- 2

~ 100

=0

teachoo
Ex 14.1,7
It is given that in a group of 3 students, the probability of 2 students
not having the same birthday is 0.992. What is the probability that the
2 students have the same birthday?
Probability that two students are not having same birthday = 0.992
Probability that two students are not having same birthday
= 1- Probability that two students are having same birthday
P({not same birthday) = 1 - P{same birthday)
0.992 = 1- P(same birthday)
P(same birthday) = 1 - 0.992
P({same birthday) = 0.008
So, probability that 2 students will have the same birthday is 0.008

Ex 14.1, 8 (i) teachoo
A bag contains 3 red balls and 5 black balls. A ball is drawn at
random from the bag. What is the probability that the ball drawn is
(i) red?
Total number of balls in the bag =5+3=8 i
Number of red balls = 3
one, . _ Number of red balis

Probability of getting a red ball = Fotal number of balls

3

“8

teackhoo
Ex 14.1, 9
A box contains 5 red marbles, 8 white marbles and 4 green marbles.
One marble is taken out of the box at random. What is the probability
that the marble taken out will be
(i) red?
Total number of marbles =5+8+4=17
Number of marbles which are white = 5
P(marble taken out is red) - Number of marbles which are red
Total number of marbles
=>
“47

teachoo
Ex 14.1, 10
A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs
2 coins and ten Rs 5 coins. If it is equally likely that one of the coins
will fall out when the bank is turned upside down, what is the
probability that the coin
(i) willbe a50 p coin?
Total number of coins in a piggy bank = 100 + 50 + 20 + 10
= 180

Number of 50 p coins = 100
Probability of getting a 50 p coin = Number of coins of 50p

Total number of coins

Ex 14.1, 11 teackoo
Gopi buys a fish from a shop for his aquarium. The shopkeeper takes
out one fish at random from a tank containing 5 male fish and 8
female fish (see the given figure). What is the 7 that the
fish taken out is a male fish? LA?
2
po
Total number of fishes in a tank gee
= Number of male fishes + Number of female fishes
=5+8
=13
Number of male fishes = 5
ope, . . . Number of male fishes
Probability of getting a male fish = Total number of fishes
22
“43

Ex 14.1, 12 teachoo
A game of chance consists of spinning an arrow which comes to
rest pointing at one of the numbers 1, 2, 3, 4,5, 6, 7, 8 (see the
given figure), and these are equally likely outcomes. What is the
probability that it will point at
(i) 8? dhy
Total numbers = 8 Ke / \3/
Number of times we can get 8 = 1 Ary
Probability of getting 8 = Number of times we can get 8
Total numbers
=i
8

Ex 14.1, 13 teachoo
A die is thrown once. Find the probability of getting
(i) a prime number; Oss
Total outcomes that can occur are 1, 2, 3, 4, 5,6 Ye
Number of possible outcomes of a dice = 6
Prime number is a number not divisible by any number except itself
Prime numbers on a dice are 2, 3, and 5.
Total prime numbers on a dice = 3
Probability of getting a prime number

_ Number of outcomes where prime number comes

~ Total number of outcomes

teachoo

Ex 14.1, 14
One card is drawn from a well-shuffled deck of 52 cards. Find the
probability of getting
(i) a king of red colour ie Be eal pet om
Total number of cards = 52
Total number of kings of red colour = 2
P (getting a king of red colour) = ee ne eee wns corona ee

22%

~ 52

21

~ 26

Ex 14.1, 15 teackhoo
Five cards--the ten, jack, queen, king and ace of diamonds, are
well-shuffled with their face downwards. One card is then picked
up at random.
(i) What is the probability that the card is the queen?
Jgwy 7 q Pag] Kwa A
‘ey | (vex) osy) |
> ECR We. per ¢
Total number of cards = 5
Number of cards that are queen = 1
: _ Number of cards that are queen
P (getting a queen) ~ Total number of cards
=i
“5s

teachoo

Ex 14.1, 16
12 defective pens are accidentally mixed with 132 good ones. It is
not possible to just look at a pen and tell whether or not it is
defective. One pen is taken out at random from this lot. Determine
the probability that the pen taken out is a good one.
Total number of pens = Total defective pens + Total good pens

=12+132

=144
Number of good pens = 132

: _ Number of good pens

P (getting a good pen) ~ Total number of pens

: teackhoo
Ex 14.1, 17 (i)
A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at
random from the lot. What is the probability that this bulb is
defective?
Total number of bulbs = 20
Total number of defective bulbs = 4
P (getting a defective bulb) = Number of defective bulbs
Total number of bulbs

-4

~ 20

-1

“5s

Ex 14.1, 18 teackoo
A box contains 90 discs which are numbered from 1 to 90. If one disc
is drawn at random from the box, find the probability that it bears
(i} a two-digit number
Total number of discs = 90
Number of two digit numbers in the discs = 10, 11, 12, 13, 14......., 90
Counting number of two digit numbers

10, 11, 12, 13, 14......., 90
Since difference between consecutive numbers is same,
These numbers form an A.P.

Ex 14.1, 19 teachoo
A child has a die whose six faces shows the letters as given below:
[>]
The die is thrown once. What is the probability of getting
(i) A?
Total number of faces on the die = 6
Number of faces having A on it = 2
. _ Number of faces having A
P (getting A) ~ Total number of faces on die
-2
“6
=i
“3

Ex 14.1, 20* (Optional) teackoo
Suppose you drop a die at random on the rectangular region
shown in Fig. 15.6. What is the probability that it will land inside
the circle with diameter 1m?
3m
"

Here, we use area to find probability
Now,

Diameter of circle = 1m

Radius of circle = ; m

Ex 14.1, 21 teackoo
A lot consists of 144 ball pens of which 20 are defective and the
others are good. Nuri will buy a pen if it is good, but will not buy if it
is defective. The shopkeeper draws one pen at random and gives it
to her. What is the probability that
(i) She will buy it?
Total number of pens = 144
Number of pens Nuri will buy

= Number of good pens

= Total number pens — Number of defective pens

= 144-20

=124

teachoo
Ex 14.1, 22
Two dice, one blue and one grey, are thrown at the same time.
(i) Write down all the possible outcomes and complete the
Event: Sum of 7 10 u |412
two dice
a 22D 38 14 1S 6 1 5 41s a2 sad
UNAM 36 3616 36°12 369 36 366 36 369 361236 18 36
Total number of outcomes = 36
Second Die
1 2 3 4 3. 6
1} (4, 7, 3-11, 41 Mi, 6)
2 Ay, 5) 1276)
. . 3 74 gS
First Die }
4 1,3) 44 4 4
5 7 2LAS, 4
6 \(6, 1) 4%. 2) e E 6, 6)

Ex 14.1, 23 teachoo
A game consists of tossing a one rupee coin 3 times and noting its
outcome each time. Hanif wins if all the tosses give the same result
i.e., three heads or three tails, and loses otherwise. Calculate the
probability that Hanif will lose the game.
Possible outcomes = (H, H, H), (H, H, T), (H, T, H), {T, H, H),
(T, T, H), (7, H, T), (H, T, T), (T, T, T)
Total possible outcomes = 8
Number of outcomes where Hanif loses the game = 8-2 =6
P (Hanif will lose the game) = Number of outcomes where Hanif loses
Total outcomes
-£ 23
“g 4

Ex 14.1, 24 teackoo
A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
Second Die
1 2 3 4 5 6
1} (1,4) (1,2) (1,3) (1,4) (1, 5)} (4, 6)
2 1(2,1) (2,2) (2,3) (2,4) |(2,5)] (2, 6)
First Die 3 (3,1) (3,2) (3,3) (3,4) |(3,5)] (3, 6)
4 1(4,1) (4,2) (4,3) (4,4) (4,5) (4, 6)
5 [(5,1) (5,2) (5,3) (5,4)
6 |(6,1) (6,2) (6,3) (6,4) (6, 6)
Total number of outcomes = 36
Total outcomes where 5 comes up = 11
Total outcomes where 5 will not come up = 36-11
=25

teachoo
Ex 14.1, 25
Which of the following arguments are correct and which are not
correct? Give reasons for your answer.
(i) lf two coins are tossed simultaneously, there are three possible
outcomes, two heads, two tails or one of each. For each of these
outcomes, the probability is > >
“re
Tails Heads
Total possible outcomes = {H, H), (H, T), (T, H), {T, T)
Number of possible outcomes = 4
Probability of getting two heads = Number of times two heads occurs
Total number of outcomes
1 1
=s=- #-
4 3

Which of the following arguments are correct and which are not correct? Give reasons for your answer. (ii) If a die is thrown, there are two possible outcomes- an odd number or an even number .Therefore the probability of getting an odd number is 1/2

Example 1 teachoo.com
Find the probability of getting a head when a coin is tossed once.
Also find the probability of getting a tail.
Total number of outcomes * “ie
= 2 (either Heads or Tails) oe
Tails Heads
Number of outcomes in which head comes = 1
P(getting a Head) = Number of outcomes in which head comes
Total Number of outcomes
=i
“2
Number of outcomes in which tail comes = 1
P(getting a Tail) = Number of outcomes in which tail comes
Total Number of outcomes
=i
“5

teachoo.com
Example 2
A bag contains a red ball, a blue ball and a yellow ball, all the balls
being of the same size. Kritika takes out a ball from the bag without
looking into it. What is the probability that she takes out the
(i) yellow ball?
Total number of balls = 3 i
Number of balls which are yellow = 1
P(ball taken out yellow) = Number of balls which are yellow
Total number of balls
=i
“3

Exampl e3 teachoo.com
Suppose we throw a die once.
(i) What is the probability of getting a number greater than 4 ?
Total outcomes that can occur are 1, 2, 3, 4,5, 6 (RS
Total number of outcomes = 6 we
Numbers greater than 4=5&6
Number of outcomes where number is greater than 4 = 2
Probability of getting a number greater than 4

_ Number of outcomes where there is anumber greater than 4

~ Total number of outcomes

=2

“6

=i

“3

teachoo.com
Example 4
One card is drawn from a well-shuffled deck of 52 cards. Calculate
the probability that the card will
(i) be an ace,
‘8
ck
my
Total number of cards = 52 ve \ fo]
Total number of aces = 4 NG
. _ Number of aces
P (getting an ace) ~ Total number of cards
4+
~ 52
=i
43

teachoo.com

Example 5
Two players, Sangeeta and Reshma, play a tennis match. It is known
that the probability of Sangeeta winning the match is 0.62. What is
the probability of Reshma winning the match?
Either Sangeeta or Reshma can win the match
P(Reshma wins) = P( Sangeeta does not win)

= 1- P(Sangeeta wins)

=1-0.62

= 0.38

teachoo.com

Example 6
Savita and Hamida are friends. What is the probability that both
will have
(i) different birthdays? (ignoring a leap year).
P(both have different birthday)

= P(both will not have same birthday)

= 1- P(both will have same birthday)

=1-4

365

_ 365-1

~ 365

— 364

~ 365

Example 7 {i) teachoo.com
There are 40 students in Class X of a school of whom 25 are girls and
15 are boys. The class teacher has to select one student as a class
representative. She writes the name of each student on a separate
card, the cards being identical. Then she puts cards in a bag and stirs
them thoroughly. She then draws one card from the bag. What is the
probability that the name written on the card is the name of
(i) agirl?
Total number of cards = Total number of students = 40
Number of cards with the name of a girl = Number of girls = 25
P (card with name of a girl) = a TT aye agirl

=-25_5

40° 8

teachoo.com
Example 8
A box contains 3 blue, 2 white, and 4 red marbles. If a marble is
drawn at random from the box, what is the probability that it will be
(i) white?
Total number of marbles = 3+2+4=9
Number of marbles which are white = 2
P(marble taken out is white) - Number of marbles which are white
Total number of marbles
=2
“9

teachoo.com

Example 9
Harpreet tosses two different coins simultaneously (say, one is of Re 1
& other of Rs 2). What is probability that she gets at feast one head?
Total possible outcomes = (H, H), (H, T), (T, H}, (T, T)
Number of possible outcomes = 4
Total outcomes where she get atleast one head = (H, H), (H, T), (T, H)
Number of outcomes where she get atleast one head = 3
P{she gets atleast one head)

_ Number of outcomes where she gets atleast one head

~ Number of possible outcomes

=?

“4

teachoo.com

Example 10* (Optional)
In a musical chair game, the person playing the music has been
advised to stop playing the music at any time within 2 minutes
after she starts playing. What is the probability that the music will
stop within the first half-minute after starting?
Let’s represent the time by straight line

—t_+—_+—_-

0 a 1 2

2

We have to find probability that music will stop within first half
minute
Here, we use distance to find probability

Example 11* (Optional) teaehoosom
A missing helicopter is reported to have crashed somewhere in
the rectangular region shown in Fig. 15.2. What is the probability
that it crashed inside the lake shown in the figure
———_ 6 km ——____ >
UEP ENERGY RE SLES
| PS{e eee SSIES
a seeps
98 er
Here, we use area to find probability
First,
let us find length and height of the lake

teachoo.com

Example 12 (i)
A carton consists of 100 shirts of which 88 are good, 8 have minor
defects and 4 have major defects. Jimmy, a trader, will only accept
the shirts which are good, but Sujatha, another trader, will only
reject the shirts which have major defects. One shirt is drawn at
random from the carton. What is the probability that
(i) itis acceptable to Jimmy?
Total number of shirts = 100
Number of shirts acceptable to jimmy

= Number of shirts which are good

= 88

teachoo.
Example 13 (i) faemooom
Two dice, one blue and one grey, are thrown at the same time.
Write down all the possible outcomes. What is the probability that
the sum of the two numbers appearing on the top of the dice is
(i) 8?
Total number of outcomes = 36
Probability that sum of two numbers is 8
_ Number of outcomes where sum is 8
~ Total number of outcomes
_5
” 36 Grey Die
1 2 3 4 5 6
1} (4,1) (4,2) (1,3) (4,4) (4,5) (1,6)
2 1(2,1) (2,2) (2,3) (2,4) (2, 2, 6)
3 1(3,1 3,2 4 ? ,
Blue Die (32) (3,2) (3,3) 3,5) 5)
4 1(4,1) (4,2) (4, (4,4)-44, 5) (4, 6)
5 1(5,1) (5, (5,3 ,4) (5,5) (5, 6)
6 | (6,1) (6, 2)-{6, 3) (6,4) (6,5) (6, 6)

This question is
inspired from
Ex 15.1, 14 - Chapter 15 Class 10
- Probability
On a weekend Rani was playing cards with her family .The deck has 52 cards. If her brother drew one card .
Question 1
Find the probability of getting a king of red colour
(a) 1/26 (b) 1/13 (c) 1/52 (d) 1/4
Question 2
Find the probability of getting a face card.
(a) 1/26 (b) 1/13 (c) 2/13 (d) 3/13
Question 3
Find the probability of getting a jack of hearts
(a) 1/26 (b) 1/52 (c) 3/52 (d) 3/26
Question 4
Find the probability of getting a red face card
(a) 3/26 (b) 1/13 (c) 1/52 (d) 1/4
Question 5
Find the probability of getting a spade.
(a) 1/26 (b) 1/13 (c) 1/52 (d) 1/4

This question is
inspired from
Example 13 - Chapter 15 Class 10
- Probability
Rahul and Ravi planned to play Business ( board game) in which they were supposed to use two dice
Question 1
Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8?
(a) 1/26 (b) 5/36 (c) 1/18 (d) 0
Question 2
Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13?
(a) 1 (b) 5/36 (c) 1/18 (d) 0
Question 3
Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12 ?
(a) 1 (b) 5/36 (c) 1/18 (d) 0
Question 4
Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7 ?
(a) 5/9 (b) 5/36 (c) 1/6 (d) 0
Question 5
Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8 ?
(a) 1 (b) 5/36 (c) 1/18 (d) 5/18

Question A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Question 1 How many triangles are of red colour and how many squares are of red colour? (a) 5, 4 (b) 4, 5 (c) 5, 5 (d) 8, 6 Given that
Game has 8 triangles of which 3 are blue & rest are red,
And 10 squares of which 6 are blue & rest are red

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is: (a) 7/90 (b) 10/90 (c) 4/45 (d) 9/89 Total number of disks = 90

The probability of getting an even number, when a die is thrown once, is: (a) 1/2 (b) 1/3 (c) 1/6 (d) 5/6 When a die is thrown
Total outcomes = 1, 2, 3, 4, 5, 6
And,
Even number = 2, 4, 6

In a family of 3 children, the probability of having at least one boy is: (a) 7/8 (b) 1/8 (c) 5/8 (d) 3/4 In a family of 3 children, the possible outcomes are
BBB
BBG
BGB
GBB
BGG
GBG
GGB
GGG

A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is: (a) 2/3 (b) 1/6 (c) 1/3 (d) 11/30 Total numbers = 30

The probability that a number selected at random from the numbers 1, 2, 3, ....., 15 is a multiple of 4, is: (a) 4/15 (b) 2/15 (c) 1/5 (d) 1/3 Total numbers = 15

Two different coins are tossed simultaneously. The probability of getting at least one head is: (a) 1/4 (b) 1/8 (c) 3/4 (d) 7/8 When 2 coins are tossed
Possible outcomes = HH, TH, HT, TT

A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is: (a) 1/5 (b) 3/25 (c) 4/25 (d) 2/25Total numbers = 25

If two different dice are rolled together, the probability of getting an even number on both dice, is: (a) 1/36 (b) 1/2 (c) 1/6 (d) 1/4 When two dice are thrown
Total outcomes = 36
Number of outcomes with even number on both dice = 3 + 3 + 3 = 9

A card is drawn at random from a pack of 52 cards. The probability that the drawn card a face card of club (A) 3/52 (B) 4/13 (C) 2/26 (D) 12/13
Total number of cards = 52

Two dice are thrown together. The Probability of getting the same number on both dice is (A) 1/2 (B) 1/3 (C) 1/6 (D) 1/12
When two dice are thrown
Total outcomes = 36
Number of outcomes with same number on both dice = 6

Which of the the following can be the probability of an event?
– 0.04 (B) 1.004
(C) 18/23 (D) 8/7
We know that
0 ≤ Probability ≤ 1

A card is selected at random from a well shuffled deck of 52
playing cards. The probability of its being a face card is
(A) 3/13 (B) 4/13 (C) 6/13 (D) 9/13

A bag contains 3 red balls, 5 white balls and 7 black balls. What
is the probability that a ball drawn from the bag at random will be neither red nor black?
(A) 1/5 (B) 1/3 (C) 7/15 (D) 8/15
Here,
P (neither red nor black) = P (white ball)

If an event cannot occur, then its probability is
(A) 1 (B) 3/4 (C) 1/2 (D) 0

Which of the following cannot be the probability of an event?
(A) 1/3 (B) 0.1 (C) 3 % (D) 17/16
We know that
0 ≤ Probability ≤ 1

An event is very unlikely to happen. Its probability is closest to
0.0001 (B) 0.001
(C) 0.01 (D) 0.1
If an event is very unlikely to happen
It’s probability will be closest to 0

If the probability of an event is p, the probability of its complementary event will be
p − 1 (B) p
(C) 1 − p (D) 1 − 1/𝑝
We know that
Probability of event + Probability of complementary event = 1
p + Probability of complementary event = 1
Probability of complementary event = 1 − p

The probability expressed as a percentage of a particular occurrence can never be
less than 100
(B) less than 0
(C) greater than 1
(D) anything but a whole number
We know that
0 ≤ Probability ≤ 1

If P(A) denotes the probability of an event A, then
P(A) < 0 (B) P(A) > 1
(C) 0 ≤ P(A) ≤ 1 (D) –1 ≤ P(A) ≤ 1
We know that
0 ≤ Probability ≤ 1

A card is selected from a deck of 52 cards. The probability of its being a red face card is
(A) 3/26 (B) 3/13
(C) 2/13 (D) 1/2
Total number of cards = 52

The probability that a non leap year selected at random will contain 53 Sundays is
(A) 1/7 (B) 2/7
(C) 3/7 (D) 5/7
A non leap year has 365 days

When a die is thrown, the probability of getting an odd number less than 3 is
(A) 1/6 (B) 1/3 (C) 1/2 (D) 0
Possible outcomes when dice is thrown are 1, 2, 3, 4, 5, 6
Odd number less than 3 is 1

A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
4 (B) 13 (C) 48 (D) 51
Given that
Event E: E is that card is not an ace of hearts
Therefore,
Event not E: E is that card is an ace of hearts

The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
7 (B) 14
(C) 21 (D) 28
Now,
Probability of getting a bad egg = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑑 𝑒𝑔𝑔𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑔𝑔𝑠)
0.035 = (𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒃𝒂𝒅 𝒆𝒈𝒈𝒔)/𝟒𝟎𝟎
0.035 × 400 = Number of bad eggs
Number of bad eggs = 0.035 × 400
Number of bad eggs = 𝟎𝟑𝟓/𝟏𝟎𝟎𝟎 × 400
Number of bad eggs = 35/10 × 4
Number of bad eggs = 140/10
Number of bad eggs = 14

A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
40 (B) 240
(C) 480 (D) 750
Now,
Probability of winning = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑐𝑘𝑒𝑡𝑠 𝑏𝑜𝑢𝑔ℎ𝑡)/(𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑐𝑘𝑒𝑡𝑠)
0.08 = (𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒕𝒊𝒄𝒌𝒆𝒕𝒔 𝒃𝒐𝒖𝒈𝒉𝒕)/𝟔𝟎𝟎𝟎
0.08 × 6000 = Number of tickets bought
Number of tickets bought = 0.08 × 6000
Number of tickets bought = 𝟖/𝟏𝟎𝟎 × 6000
Number of tickets bought = 8 × 60
Number of tickets bought = 480

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
(A) 1/5 (B) 3/5
(C) 4/5 (D) 1/3
Total number of tickets = 40

Someone is asked to take a number from 1 to 100. The probability that it is a prime is
(A) 1/5 (B) 6/25
(C) 1/4 (D) 13/50
Total numbers = 100

A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is
(A) 4/23 (B) 6/23 (C) 8/23 (D) 17/23
Now,
Number of students in A = 4
Number of students in B = 8
Number of students in C = 5
Number of students in D = 2
Number of students in E = 23 − (4 + 8 + 5 + 2) = 4
Now,
Probability that the selected student is not from A, B and C
= P(student is from D and E)
= (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝐷 𝑎𝑛𝑑 𝐸)/(𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑡𝑢𝑑𝑒𝑛𝑡𝑠)
= (2 + 4)/23
= 𝟔/𝟐𝟑

Ex 15.2, 1 teachoo.com
Two customers Shyam and Ekta are visiting a particular shop in
the same week (Tuesday to Saturday). Each is equally likely to visit
the shop on any day as on another day. What is the probability
that both will visit the shop on
(i) the same day?
(ii) consecutive days?
(ili) different days?
Shyam and Ekta can visit the shop on Tuesday, Wednesday,
Thursday, Friday & Saturday.
Let T = Tuesday, W = Wednesday, Th = Thursday, F = Friday and
S = Saturday.
Then, total possible outcomes are
(T, T) (T, W) (T, Th) (T, F) (T, S)
(W, T) (W,W) (W,Th) (WF) (W, S)

teachoo.com
Ex 15.2, 2
A die is numbered in such a way that its faces show the
numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total
score in two throws is noted. Complete the following table
which gives a few values of the total scores on the two throws:
Number in first throw

3 1 2 2 3 3 6

g— 1] 2 3 3 4 4 7

E 2] 3 4 4 5 5 8

3

& 2 5

£

. 3

ou

a

—E 3 5 9

3

= 6| 7 8 8 9 9 12
What is the Probability that the total score is
(i) even ? (ii) 6? (iii) at least 6?
Possible results on 2 throws of a die are 1, 2,3 & 6.

teachoo.com

Ex 15.2,3
A bag contains 5 red balls and some blue balls. If the probability
of drawing a blue ball is double that of a red ball, determine the
number of blue balls in the bag.
The bag contains red and blue balls.

Number of red balls = 5
Let Number of blue balls = x
- Total number of balls = 5 +x
Given,

Probability of drawing a blue ball is double that of a red ball.

Probability of drawing blue ball = 2 x Probability of drawing red ball

Ex 15.2, 4 teachoo.com
A box contains 12 balls out of which x are black. If one ball is
drawn at random from the box, what is the probability that it will
be a biack ball?
tf 6 more black balls are put in the bag, the probability of
drawing a black ball is now double of what is was before. Find x.
Given,
Total balls in the box = 12
Black balls in the box = x
Probability of drawing a black ball = Number of Pack balls
Total number of balls
= «=
~ 42
If 6 more black balls are put in the box,
Total number of balls = 12 +6 = 18

teach
Ex 15.2, 5 vam fom
A jar contains 24 marbles, some are green and other are blue. If
a marble is drawn at random from jar, the probability that it is
greenis >. Find the number of blue bails in the jar.
Total number of marbles = 24
Let number of green marbles = x
Then, Number of blue marbles = 24 — x
Given, probability of drawing a green marbles =;
Number of greenmarbles _ 2
Total Number of marbles ~ 3
* 22
243
x =2x24
3