Multiple choice

Two dice are thrown. The probability that the sum of the numbers coming up on them is $9$, if it is known that the number $5$ always occurs on the first die, is

  1. $\displaystyle \frac { 1 }{ 6 } $
  2. $\displaystyle \frac { 1 }{ 3 } $
  3. $\displaystyle \frac { 1 }{ 2 } $
  4. $\displaystyle \frac { 5 }{ 6 } $
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A Correct answer
Explanation

Sample space given 5 on first die: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6). Total = 6. Favorable outcome for sum 9: (5,4). Probability = 1/6.

AI explanation

Using the conditional probability formula, we restrict our sample space to the 6 outcomes where the first die is a 5. To achieve a sum of 9 with the first die being 5, the second die must show a 4, which is exactly 1 favorable outcome. The conditional probability is therefore 1 divided by 6.

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