Multiple choice

A pair of dice is thrown. If the sum of numbers that turned up on the two dice is $8$, then the probability that the number upon the second die is $5$ is ?

  1. $\dfrac{5}{36}$
  2. $\dfrac{1}{6}$
  3. $\dfrac{1}{5}$
  4. $\dfrac{2}{5}$
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C Correct answer
Explanation

Total outcomes with sum 8: (2,6), (3,5), (4,4), (5,3), (6,2). There are 5 outcomes. The event where the second die is 5 is (3,5). Probability = 1/5.

AI explanation

We use the conditional probability formula. The combinations that yield a sum of 8 are (2, 6), (3, 5), (4, 4), (5, 3) and (6, 2), giving 5 total possible outcomes. Out of these, only the outcome (3, 5) has the number 5 on the second die. The required probability is therefore 1 divided by 5.

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