Question

Events A and B are mutually exclusive. Suppose event A occurs with probability 0.82 and event B occurs with probability 0.03. Compute the probability that A occurs or B does not occur (or both). Compute the probability that either A occurs without B occurring or A and B both occur.

Answer 1

P(A) = 0.82

P(B) = 0.03

As A and B are mutually exclusive so P(both) = 0

a) P(A occurs or B does not accur) = P(B doesn't occur) = 1 - P(B) = 1 - 0.03 = 0.97

If B doesn't occur then that will contain entire A occurs because A and B are mutually exclusive.

b) P(either A occurs without B or both) = P(A occurs) = 0.82

Since A and B are both cannot occur hence there is no value of 'both' condition and A is occurring with B always.

I hope this will help. Thank you.