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Three cards are drawn successively from a pack of 52 well shuffled

Example 9 - Chapter 13 Class 12 Probability - Part 2
Example 9 - Chapter 13 Class 12 Probability - Part 3 Example 9 - Chapter 13 Class 12 Probability - Part 4 Example 9 - Chapter 13 Class 12 Probability - Part 5

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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 Finding Probabilities separately Probability first card is king Number of kings in a pack of 52 cards = 4 So, Probability = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑘𝑖𝑛𝑔𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠) = (4 )/52 = 1/13 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 So, Probability = 3/51 = 1/17 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 So, Probability = 4/50 = 2/25 Therefore, 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 = 𝟏/𝟏𝟑 × 𝟏/𝟏𝟕 × 𝟐/𝟐𝟓 = 𝟐/𝟓𝟓𝟐𝟓

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.