Two packs of cards are thoroughly mixed and stuffed and two cards are drawn at random, one after the other. What is the probability that both of them are Jacks?

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Submitted by examrobotsa on

Q: 149 (IAS/1996)
Two packs of cards are thoroughly mixed and stuffed and two cards are drawn at random, one after the other. What is the probability that both of them are Jacks?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,6,4,0,2,6,2

keywords: 

{'probability': [0, 3, 3, 0], 'jacks': [0, 1, 0, 0], 'cards': [1, 1, 0, 2], 'packs': [0, 1, 0, 0]}

The process of picking two Jacks from two shuffled decks involves calculating the probability of two independent events. Since there are four Jacks in each deck, there are eight Jacks in two decks. So, the probability of the first card being a Jack is 8 out of 104 (since there are 104 cards in total). After one Jack is selected, there are now 7 Jacks left out of 103 remaining cards.

This leads to the probability of (8/104) for the first card and (7/103) for the second card. The probability of both events occurring is the multiple of the two, giving (8/104) * (7/103) = 56/10672 = 7/1339.

Option 1 and 2 which is 1/13 and 2/13 respectively, do not account for the second event`s probability of increasingly lower chance since there are fewer Jacks and fewer total cards left. Option 4 which is 1/169 also does not match our calculated probability. Hence, option 3, which is 7/1339 is correct.