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?
Reviewed by Dalvoy
UPSC Civil Services preparation
- A1/13
- B2/13
- C7/1339Correct
- D1/169
Explanation
To find the probability, we first determine the total number of cards and the number of Jacks available.
1. Total cards: Since there are two packs, the total number of cards is 52 plus 52, which equals 104.
2. Total Jacks: Each pack has 4 Jacks, so two packs have 8 Jacks in total.
3. First draw: The probability of drawing a Jack is 8 out of 104. This simplifies to 1 out of 13.
4. Second draw: Since one Jack has already been removed, there are now 7 Jacks left and 103 total cards remaining. The probability of drawing a second Jack is 7 out of 103.
5. Combined probability: To find the final answer, multiply the two probabilities together. 1 divided by 13 multiplied by 7 divided by 103 equals 7 divided by 1339.
Therefore, option C is the correct answer.
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