Multiple choice

Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are red or both are jacks?

  1. 330/1225

  2. 1/1326

  3. 332/1326

  4. 55/221

  5. 331/1326
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D Correct answer
Explanation

Using the inclusion-exclusion principle, P(A or B) = P(A) + P(B) - P(A and B). P(both red) = (26/52) * (25/51) = 325/1326. P(both jacks) = (4/52) * (3/51) = 12/1326. P(both red and both jacks) = P(both red jacks) = (2/52) * (1/51) = 2/1326. Total probability = (325 + 12 - 2) / 1326 = 335/1326. This simplifies to 55/221.

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