Question

Events A and B are mutually exclusive. Suppose event A occurs with probability 0.18 and event B occurs with probability 0.64.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.

Answer 1

Anic, let's find the solution:

P (A) = 0.18

P (A does not occur) = 1 - 0.18 = 0.82

P (B) = 0.64

P (B does not occur) = 1 - 0.64 = 0.36

a. Compute the probability that B occurs or A does not occur (or both).

A and B are mutually exclusive events, therefore:

P (B or A does not occur) = P(B) + P (A does not occur) - P (B and A does not occur)

P (B or A does not occur) = 0.64 + 0.82 - (0.64 * 0.82)

P (B or A does not occur) = 0.64 + 0.82 - 0.5248

P (B or A does not occur) =0.9352

b. Compute the probability that either B occurs without A occurring or A and B both occur.

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

P (B or A and B) = 0.64 + (0.64 * 0.18) - (0.64 * 0.1152)

P (B or A and B) = 0.64 + 0.1152 - (0.64 * 0.1152)

P (B or A and B) = 0.64 + 0.1152 - 0.0737

P (B or A and B) = 0.6815