Question

Suppose two standard die are rolled and it is known that one of the die landed on a four. What is the probability that the sum of the die is a prime number?

Answer 1

The probability that the sum of two dice is a prime number given one die landed on a four is 2 out of 5 or 0.4.

Step-by-step explanation:

Given that one die has landed on a four, we need to calculate the probability that the sum of two dice is a prime number. When we know one die is a four, the possible outcomes for the sum are 5, 6, 7, 8, 9, and 10, when the second die lands on 1, 2, 3, 4, 5, and 6, respectively. The prime numbers from these sums are 5, 7, and 11. Since we know the second die cannot be a four (as it is the first die), we remove that outcome, leaving us with 5 and 7 as the prime sums. The combinations leading to these sums are (4,1) and (4,3), out of the five possible outcomes (since (4,4) is not considered). Consequently, the probability is 2 out of 5, or 0.4.