Example 10 - Chapter 16 Class 11 Probability (Term 2)
Last updated at Feb. 11, 2020 by Teachoo
Last updated at Feb. 11, 2020 by Teachoo
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Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐ ๐๐๐๐๐ )/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐ ) = (n(A))/(n(S)) = 13/52 = ๐/๐ Example 10 One card is drawn from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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