Example 9 - Three cards are drawn successively - Chapter 13 - Examples

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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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 𝑘𝑖𝑛𝑔𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = 4 ﷮52﷯ = 1﷮13﷯ 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) = 3﷮51﷯ = 1﷮17﷯ 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) = 4﷮50﷯ = 2﷮25﷯ Now, P(KKA) = P(K) × P(K|K) × P(A|KK) = 𝟏﷮𝟏𝟑﷯ × 𝟏﷮𝟏𝟕﷯ × 𝟐﷮𝟐𝟓﷯ = 𝟐﷮𝟓𝟓𝟐𝟓﷯ ∴ P(KKA) = 2﷮5525﷯

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