Check sibling questions

Example 10 - One card is drawn from a well shuffled deck

Example 10 - Chapter 16 Class 11 Probability - Part 2
Example 10 - Chapter 16 Class 11 Probability - Part 3
Example 10 - Chapter 16 Class 11 Probability - Part 4
Example 10 - Chapter 16 Class 11 Probability - Part 5
Example 10 - Chapter 16 Class 11 Probability - Part 6
Example 10 - Chapter 16 Class 11 Probability - Part 7
Example 10 - Chapter 16 Class 11 Probability - Part 8

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Transcript

Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be a diamond Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑎𝑚𝑜𝑛𝑑 𝑐𝑎𝑟𝑑𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠) = (n(A))/(n(S)) = 13/52 = 𝟏/𝟒 Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (ii) not an ace There are 4 ace cards Let B be the event that card drawn is ace So, n(B) = 4 Hence Probability card drawn is ace = P(B) = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑒 𝑐𝑎𝑟𝑑𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠) = (n(A))/(n(S)) = 4/52 = 1/13 Probability that card is not an ace = P(B’) = 1 – P(B) = 1 – 1/13 = (13 − 1)/13 = 𝟏𝟐/𝟏𝟑 Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (iii) a black card (i.e., a club or, a spade) There are 26 black cards (13 spade and 13 club) Let C be the probability that card drawn is black n(C) = 13 + 13 = 26 Hence Probability card drawn is black = P(C) = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑎𝑐𝑘 𝑐𝑎𝑟𝑑𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠) = (n(C))/(n(S)) = 26/52 = 𝟏/𝟐 Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (iv) not a diamond From part (i) , A is the event that card is diamond So, A’ is event that card is not diamond Probability card is not a diamond = P(A’) = 1 – P(A) = 1 – 1/4 = (4 − 1)/4 = 𝟑/𝟒 Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (v) not a black card From part (iii) , C is the event that card is black So, C’ is event that card is not black Probability card is not a black = P(C’) = 1 – P(C) = 1 – 1/2 = 𝟏/𝟐

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.