UPSC Prelims 1996 · General Studies
Question 149: Basic Numeracy
Two packs of cards are thoroughly mixed and shuffled and two cards are drawn at random, one after the other. What is the probability that both of them are Jacks?
AnswerThe answer is (c).
Two packs have 104 cards, including 8 Jacks. The probability that the first card is a Jack is 8/104; with one Jack gone, the second is a Jack with probability 7/103. The product is 56/10712, which reduces to 7/1339. Remember: the cards are drawn one after the other without replacement, so the second probability uses 103 cards.
Why each option is right or wrong
- (a) 1/13 is the chance of one Jack in a single draw; both Jacks need the product of two chances.
- (b) 2/13 is not the product of two draw probabilities.
- (c) Right: (8/104) x (7/103) = 7/1339.
- (d) 1/169 treats the draws as independent with 1/13 each, ignoring that a card is removed.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 1996, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.