Multiple choice

One card is drawn from each of two ordinary sets of 52 cards.Find the probability that at least one of them will be Ace of hearts.

  1. $\displaystyle \frac{1}{52}$
  2. $\displaystyle \frac{1}{26}$
  3. $\displaystyle \frac{103}{2704}$
  4. $\displaystyle \frac{824}{2704}$
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C Correct answer
Explanation

Probability of NOT getting Ace of hearts in one draw is 51/52. Probability of NOT getting it in two draws is (51/52) * (51/52) = 2601/2704. Probability of at least one Ace of hearts = 1 - 2601/2704 = 103/2704.

AI explanation

The probability of not drawing the Ace of hearts from a single deck is 51/52. For two independently drawn cards, the probability that neither is the Ace of hearts is (51/52) * (51/52) = 2601/2704. Using the complement rule, the probability that at least one is the Ace of hearts is 1 - 2601/2704 = 103/2704.

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