Multiple choice

Cards are drawn one by one without replacement from a well shuffled pack of $52$ cards. Then, the probability that a face card (jack,queen or king) will appear for the first time on the third turn is equal to

  1. $\cfrac{300}{2197}$
  2. $\cfrac{36}{85}$
  3. $\cfrac{12}{85}$
  4. $\cfrac{4}{51}$
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C Correct answer
Explanation

Total cards = 52, face cards = 12, non-face cards = 40. Probability = (P(non-face on 1st) * P(non-face on 2nd) * P(face on 3rd)) = (40/52) * (39/51) * (12/50) = (10/13) * (13/17) * (6/25) = (10 * 6) / (17 * 25) = 60 / 425 = 12 / 85.

AI explanation

The probability that the first two cards are non-face cards is 40/52 multiplied by 39/51. The probability that the third card is a face card is 12/50. Multiplying these gives (40/52) * (39/51) * (12/50), which simplifies to 12/85.

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