Explanation:
The sample space for rolling two dice consists of 36 possible outcomes, as each of the six faces on the first die can be combined with any of the six faces on the second die.
To find the probability of showing either a prime number on the first die or a multiple of 5 on the second die, we can use the principle of inclusion-exclusion.
There are 3 prime numbers on a standard die: 2, 3, and 5. And there are two multiples of 5: 5 and 10. However, we need to be careful not to count the outcome (5,5) twice, as it satisfies both conditions.
So, the probability of showing either a prime number on the first die or a multiple of 5 on the second die is:
P(prime or multiple of 5) = P(prime) + P(multiple of 5) - P(prime and multiple of 5)
P(prime) = 3/6 = 1/2
P(multiple of 5) = 2/6 = 1/3
P(prime and multiple of 5) = 1/36
Therefore,
P(prime or multiple of 5) = 1/2 + 1/3 - 1/36
= 19/36
So the probability of showing either a prime number on the first die or a multiple of 5 on the second die is 19/36, or approximately 0.528.