Question

Events 4 and B are mutually exclusive. Suppose event A occurs with probability 0.52 and event B occurs with probability 0.13, a. Compute the probability that A occurs or B does not occur (or both). b. Compute the probability that either A occurs without B occurring or A and B both occur.

Answer 1

Please read the answer below. Don't hesitate to give a "thumbs up" in case you're satisfied with the answer.

a. P(A occurs or B does not occur)

Since A and B are mutually exclusive B' will encompass A too.

So, P(A occurs or B does not occur) = P(B') = 1-P(B) = 1-.13 = .87

b. P(either A occurs without B occuring or A and B both occur)

A occurs without B occuring = A occurs, as A and B are mutually exclusive

A and B occur is a null set, as A and B are Mutually Exclusive , they both can't occur together

So, P(either A occurs without B occuring or A and B both occur) reduces to = P(A or Nullset) = P(A) = .52