Question

a set containing an 8 when a regular die is rolled”​

Answer 1

What is the probability of rolling an 8 when rolling a standard die?

Two (6-sided) dice roll probability table

Roll a… Probability

8      26/36 (72.222%)

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Answer 2

first die to be prime and the first die to have a total of eight, which is how I first read your question, then the probability is 0 since one die can’t “total” over 6.

On the other hand, if you meant for the first die to be prime or for the total of the two dice to be eight then

P(prime number) = P(2, 3, 5) = 3/6 = 1/2

Die rolls that total eight: (2, 4), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (4, 2)

P(total eight) = 7 / 36

Die rolls that total eight and have a first prime number: (2, 4), (2, 6), (3, 5), (5, 3)

P(first prime number and total of eight) = 4 / 36

P(first prime number or total of eight) = P(first prime number) + P(total of eight) - P(first prime number and total of eight) = 1/2 + 7/36 - 4/36 = 18/36 + 7/36 - 4/36 = 21/36 = 7/12.