Multiple choice

Two cards are drawn together from a pack of52 cards. The probability that one is a spade andone is a heart, is

  1. 29/34

  2. 47/100

  3. 3/20

  4. 13/102

  5. 1/21
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D Correct answer
Explanation

Total ways to choose 2 cards from 52 is 52C2 = 1326. Ways to choose 1 spade (13) and 1 heart (13) is 13 * 13 = 169. Probability = 169 / 1326 = 13 / 102.

AI explanation

The total number of ways to draw two cards from a pack of 52 is given by the combination formula 52C2, which equals 1326. The number of ways to draw one spade and one heart is 13C1 multiplied by 13C1, yielding 169 favorable outcomes. Using the classical definition of probability, we divide the favorable outcomes by the total outcomes to get 169/1326, which simplifies to 13/102.

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