Multiple choice

Two cards are drawn from a well shuffled pack of 52 playing cards one by one. If $A$: the event that the second card drawn is an ace and $B$: the event that the first card drawn is an ace card. then which of the following is true?

  1. $P(A)=\displaystyle \frac {4}{17}; P(B)=\frac {1}{13}$
  2. $P(A)=\displaystyle \frac {1}{13}; P(B)=\frac {1}{13}$
  3. $P(A)=\displaystyle \frac {1}{13}; P(B)=\frac {1}{17}$
  4. $P(A)=\displaystyle \frac {16}{221}; P(B)=\frac {4}{51}$
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B Correct answer
Explanation

P(B) = 4/52 = 1/13. P(A) is the probability the second card is an ace. By symmetry, the probability of any specific card being an ace is 4/52 = 1/13. Thus P(A) = 1/13.

AI explanation

The probability of drawing an ace on the first draw is 4 out of 52, which simplifies to 1/13. By the law of total probability, the probability that the second card is an ace is the sum of two conditional probabilities: (4/52)(3/51) + (48/52)(4/51). Calculating this gives 12/2652 + 192/2652, which equals 204/2652, simplifying exactly to 1/13. Therefore, both P(A) and P(B) equal 1/13.

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