# Example 9

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 9 Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace? Probability first two cards are king & third drawn is ace = Probability first card is king × Probability second card is king , if first card is king × Probability third card is ace, if first two are kings So, P(KKA) = P(K) × P(K|K) × P(A|KK) Now, P(K) = Probability that first card is king Number of kings in a pack of 52 cards = 4 ∴ P(K) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑘𝑖𝑛𝑔𝑠𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠 = 4 52 = 113 P(K|K) = Probability that the second card drawn is king, if the first card drawn has a king If first card drawn has king, Total number of kings left in the pack = 3 & Total number of cards in the pack = 51 ∴ P(K|K) = 351 = 117 P(A|KK) = Probability that the third card is an ace, given first two cards were kings If first two card drawn were kings, Total number of aces left in the pack = 4 & Total number of cards in the pack = 50 ∴ P(A|KK) = 450 = 225 Now, P(KKA) = P(K) × P(K|K) × P(A|KK) = 𝟏𝟏𝟑 × 𝟏𝟏𝟕 × 𝟐𝟐𝟓 = 𝟐𝟓𝟓𝟐𝟓 ∴ P(KKA) = 25525

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Chapter 13 Class 12 Probability

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.