Multiple choice

If two cards are drawn simultaneously from the same set, the probability that atleast one of them will be the ace of hearts is.

  1. $\displaystyle\frac{1}{13}$
  2. $\displaystyle\frac{1}{26}$
  3. $\displaystyle\frac{1}{52}$
  4. $\displaystyle\frac{3}{13}$
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B Correct answer
Explanation

The probability that neither card is the ace of hearts is (51/52) * (50/51) = 50/52 = 25/26. The probability that at least one is the ace of hearts is 1 - 25/26 = 1/26.

AI explanation

Using the complementary event approach, the probability that neither card is the ace of hearts is choosing 2 cards from the remaining 51 cards, calculated as 51C2 / 52C2 = (51 * 50) / (52 * 51) = 50/52. The probability that at least one card is the ace of hearts is 1 - 50/52 = 2/52 = 1/26.

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