Final answer:
The correct answer is option (b) 1/6. Given that the first die shows a 5 and the sum is 9, the second die must show a 4, which has a probability of 1/6 on a fair six-sided die.
Step-by-step explanation:
The correct answer is option b) 1/6. Since the first die shows a 5 and we know the sum of the two dice is 9, the only way to achieve this sum is if the second die shows a 4. Since a single die has six faces, each numbered from 1 to 6, and each outcome is equally likely, the probability of rolling any specific number is 1 out of 6. Therefore, the probability of the second die showing a 4 is 1/6.
When the first die shows a 5 and the sum of the faces is 9, it means that the second die must show a 4 in order to achieve a sum of 9. Since there are 6 possible outcomes for the second die (numbers 1 to 6), and only 1 of them is a 4, the probability of rolling a 4 on the second die is 1/6.
Therefore, the probability that the second die shows a 4 is 1/6.