Events A and B are mutually exclusive. Suppose event A occurs with probability 0.19 and event B occurs with probability 0.8.Compute the following.(If necessary, consult a list of formulas.)(a) Compute the probability that B occurs but A does not occur.(b) Compute the probability that either A occurs without B occurring or B occurs without A occurring.

(a) To compute the probability that event B occurs but event A does not occur, we can use the formula for the probability of the complement of an event. The complement of event A, denoted as A', represents the event that A does not occur. Since events A and B are mutually exclusive, the probability of B occurring but A not occurring is equal to the probability of event B occurring minus the probability of both A and B occurring.

Therefore, the probability that B occurs but A does not occur can be calculated as follows:

P(B and not A) = P(B) - P(A and B)

Given that P(A) = 0.19 and P(B) = 0.8, we need to find P(A and B). However, since events A and B are mutually exclusive, the probability of both A and B occurring is 0. Therefore:

P(B and not A) = P(B) - P(A and B) = 0.8 - 0 = 0.8

So, the probability that B occurs but A does not occur is 0.8.

(b) To compute the probability that either A occurs without B occurring or B occurs without A occurring, we can use the formula for the probability of the union of two events. The union of events A and B, denoted as A U B, represents the event that either A occurs, B occurs, or both occur.

Therefore, the probability that either A occurs without B occurring or B occurs without A occurring can be calculated as follows:

P(A U B) = P(A) + P(B) - P(A and B)

Given that P(A) = 0.19 and P(B) = 0.8, we need to find P(A and B). However, since events A and B are mutually exclusive, the probability of both A and B occurring is 0. Therefore:

P(A U B) = P(A) + P(B) - P(A and B) = 0.19 + 0.8 - 0 = 0.99

So, the probability that either A occurs without B occurring or B occurs without A occurring is 0.99.