Multiple choice

A pair of die is rolled up. If the sum of two dies is $10$, find the probability that one of the die showed $4$.

  1. $\dfrac{1}{3}$
  2. $\dfrac{7}{128}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{7}{28}$
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C Correct answer
Explanation

Possible pairs summing to 10: (4,6), (5,5), (6,4). Total outcomes = 3. Favorable outcomes (one die is 4): (4,6) and (6,4). Probability = 2/3.

AI explanation

When two dice are rolled, the possible outcomes giving a sum of 10 are (4, 6), (6, 4), and (5, 5), making the sample space size 3. The favorable outcomes where one die shows a 4 are (4, 6) and (6, 4), giving 2 favorable results. Using the conditional probability formula, the probability is 2 divided by 3. The result is 2/3.

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