Events A and B are mutually exclusive. Suppose event A occurs with probability 0.28 and event B occurs with probability 0.5.Compute the following.(If necessary, consult a list of formulas.)(a) Compute the probability that B occurs or A does not occur (or both).(b) Compute the probability that either B occurs without A occurring or A and B both occur.

(a) To compute the probability that B occurs or A does not occur (or both), we can use the formula for the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A ∩ B) represents the probability of both events A and B occurring simultaneously.

Given that events A and B are mutually exclusive, meaning they cannot occur at the same time, we know that P(A ∩ B) = 0.

Therefore, the probability that B occurs or A does not occur (or both) can be calculated as follows: P(B or not A) = P(B) + P(not A) - P(A ∩ B) = P(B) + P(not A) - 0 = P(B) + P(not A) = 0.5 + (1 - P(A)) = 0.5 + (1 - 0.28) = 0.5 + 0.72 = 1.22

So, the probability that B occurs or A does not occur (or both) is 1.22.

(b) To compute the probability that either B occurs without A occurring or A and B both occur, we can use the formula for the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Given that events A and B are mutually exclusive, we know that P(A ∩ B) = 0.

Therefore, the probability that either B occurs without A occurring or A and B both occur can be calculated as follows: P((B and not A) or (A and B)) = P(B and not A) + P(A and B) = P(B) - P(A ∩ B) + P(A ∩ B) = P(B) = 0.5

So, the probability that either B occurs without A occurring or A and B both occur is 0.5.