Multiple choice

One card is drawn from a well-shuffled deck of $52$ cards. Find the probability of getting neither a diamond nor a jack.

  1. $\dfrac{8}{13}$
  2. $\dfrac{9}{13}$
  3. $\dfrac{6}{13}$
  4. $\dfrac{7}{26}$
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B Correct answer
Explanation

Total cards = 52. Diamonds = 13. Jacks = 4. One jack is a diamond, so there are 13 + 3 = 16 cards that are either a diamond or a jack. The number of cards that are neither is 52 - 16 = 36. Probability = 36/52 = 9/13.

AI explanation

A standard deck has 52 cards, and the event of drawing a diamond or a jack covers 13 diamonds plus 3 additional jacks from other suits, totaling 16 cards. The probability of drawing a diamond or a jack is therefore 16/52. Using the complementary probability rule, the probability of getting neither a diamond nor a jack is 1 minus 16/52, which equals 36/52. Simplifying this fraction by dividing by 4 yields 9/13.

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