Question 4 - Case Based Questions (MCQ) - Chapter 13 Class 12 Probability

Last updated at March 16, 2023 by Teachoo

Question

A group of people start playing cards. And as weΒ know a well shuffled pack of cards contains a totalΒ of 52 cards. Then 2 cards are drawn simultaneouslyΒ (or successively without replacement).

Based on the above information answer theΒ following:

Question A group of people start playing cards. And as we know a well shuffled pack of cards contains a total of 52 cards. Then 2 cards are drawn simultaneously (or successively without replacement). Based on the above information answer the following:
Total number of ways to draw 2 cards out of 52 is
Total ways = 52C2
= 52!/(2! (52 β 2)!)
= 52!/(2! (50)!)
= 1326
Question 1 If X = no. of kings = 0, 1, 2. Then P(X = 0) =? (A) 188/221 (B) 198/223 (C) 197/290 (D) 187/221
P(X = 0)
i.e. Probability of getting 0 kings
Number of ways to get 0 kings
= Number of ways to select 2 cards out of non king cards
= Number of ways to select 2 cards out of (52 β 4 = ) 48 cards
= 48C2
= 48!/(2! (48 β 2)!)
= 48!/(2! (46)!)
= 1128
P(X = 0) = (ππ’ππππ ππ π€ππ¦π π‘π πππ‘ 0 πππππ )/(πππ‘ππ ππ’ππππ ππ π€ππ¦π )
= 1128/1326
= πππ/πππ
So, the correct answer is (a)
Question 2 If X = no. of kings = 0, 1, 2. Then P(X = 1) =? (A) 32/229 (B) 32/227 (C) 32/221 (D) 32/219
P(X = 1)
i.e. Probability of getting 1 king
Number of ways to get 1 king
= Number of ways to select 1 king out of 4 king cards Γ Number of ways to select 1 card from 48 non king cards
= 4C1 Γ 48C1
= 4 Γ 48
= 192
P(X = 1) = (ππ’ππππ ππ π€ππ¦π π‘π πππ‘ 1 ππππ)/(πππ‘ππ ππ’ππππ ππ π€ππ¦π )
= 192/1326
= ππ/πππ
So, the correct answer is (c)
Question 3 If X = no. of kings = 0, 1, 2. Then P(X = 2) =? (A) 2/219 (B) 1/221 (C) 3/209 (D) 1/209 P(X = 2)
i.e. Probability of getting 2 kings
Number of ways to get 2 kings
= Number of ways of selecting 2 kings out of 4 king cards
= 4C2
= 4!/(2! 2!)
= 6
P(X = 2) = (ππ’ππππ ππ π€ππ¦π π‘π πππ‘ 2 πππππ )/(πππ‘ππ ππ’ππππ ππ π€ππ¦π )
= 6/1326
= π/πππ
So, the correct answer is (b)
Question 4 Find the mean of the number of Kings? (A) 2/13 (B) 1/13 (C) 1/17 (D) 2/17 The probability distribution is
The expectation value E(X) is given by
π="E(X)"=β2_(π = 1)^πβππππ
= 0 Γ 188/221 +"1 Γ" 32/221 + 2 Γ 1/221
= 0 + (32+2 )/221
= 34/221
= π/ππ
So, the correct answer is (a)
Question 5 Find the variance of the number of Kings? (A) 400/2873 (B) 400/2877 (C) 400/2879 (D) 400/2871 The variance of x is given by :
Var (π)=πΈ(π^2 )β[πΈ(π)]^2
Finding π¬(πΏ^π )
E(πΏ^π )=β2_(π = 1)^πβγγπ₯_πγ^2 ππγ
= 02 Γ 188/221+"12 Γ " 32/221+ 22 Γ 1/221= 0+(32 + 4 )/221
= ππ/πππ
Now,
Var (πΏ)=π¬(πΏ^π )β[π¬(πΏ)]^π
= 36/221β(34/221)^2
= 1/221 [36βγ34γ^2/221]
= 1/221 [(221 Γ 36 β 1156)/221]
= 6800/(221)^2
= πππ/ππππ
So, the correct answer is (A)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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