What is the probability of A and B, given that P(A or B) = 0.58, P(A) = 0.6, and P(B) = 0.75?

To find the probability of both events A and B occurring, represented as P(A and B), we can utilize the principle of inclusion-exclusion in probability, which states:

P(A or B) = P(A) + P(B) - P(A and B).

Here, we are given P(A or B) = 0.58, P(A) = 0.6, and P(B) = 0.75. We can rearrange the formula to solve for P(A and B):

P(A and B) = P(A) + P(B) - P(A or B).

Now, substituting the values into the equation:

P(A and B) = 0.6 + 0.75 - 0.58.

Calculating this gives:

P(A and B) = 1.35 - 0.58 = 0.77.

Thus, the probability of both events A and B occurring is 0.77. This aligns with the correct answer provided.

Choices that were not selected likely did not yield the correct calculation based on the inclusion-exclusion principle.