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Last updated at Feb. 11, 2020 by Teachoo

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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Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ) = (n(A))/(n(S)) = 13/52 = ๐/๐ Example 10 One card is drawn from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) = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ) = (n(A))/(n(S)) = 4/52 = 1/13 Probability that card is not an ace = P(Bโ) = 1 โ P(B) = 1 โ 1/13 = (13 โ 1)/13 = ๐๐/๐๐ 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) = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ) = (n(C))/(n(S)) = 26/52 = ๐/๐ 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, Aโ is event that card is not diamond Probability card is not a diamond = P(Aโ) = 1 โ P(A) = 1 โ 1/4 = (4 โ 1)/4 = ๐/๐ 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, Cโ is event that card is not black Probability card is not a black = P(Cโ) = 1 โ P(C) = 1 โ 1/2 = ๐/๐

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.