Multiple choice

In selecting 2 cards one at a time with replacement from pack of cards, the probability that the second card is a black card, given that the first card was a red card is

  1. $\displaystyle \frac{1}{13}$
  2. $\displaystyle \frac{1}{2}$
  3. $\displaystyle \frac{1}{39}$
  4. $\displaystyle \frac{1}{8}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the selection is with replacement, the events are independent. The probability of the second card being black is independent of the first card being red. There are 26 black cards in a 52-card deck, so the probability is 26/52 = 1/2.

AI explanation

Because the first card is put back, the second draw is an independent event and the pack again has 26 black cards out of 52. Using the classical definition of probability, the required probability is 26 divided by 52. The result is 1/2.

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