Question

Events A and B are mutually exclusive. Suppose event A occurs with probability 0.02 and event B occurs with probability 0.73. Compute the probability that B occurs or A does not occur (or both). Compute the probability that either B occurs without A occurring or A and B both occur

Answer 1

Answer:

1. The probability that B occurs or A does not occur (or both) is 0.73.

2. The probability that either B occurs without A occurring or A and B both occur is 0.73.

Step-by-step explanation:

It is given that the events A and B are mutually exclusive. It means the intersection of A and B is 0.

$P(A\cap B)=0$

Given information:

$P(A)=0.02$

$P(B)=0.73$

We get,

$P(A')=1-P(A)=1-0.02=0.98$

$P(B')=1-P(B)=1-0.73=0.27$

(1) We need to find the probability that B occurs or A does not occur (or both).

$P(B\cup A')+P(A\cap B)=P(B)+0$

$P(B\cup A')+P(A\cap B)=0.73+0$

$P(B\cup A')+P(A\cap B)=0.73$

Therefore the probability that B occurs or A does not occur (or both) is 0.73.

(2) We need to find the probability that either B occurs without A occurring or A and B both occur.

$P(B\cup A')+P(A\cap B)=P(B)+0$

$P(B\cup A')+P(A\cap B)=0.73+0$

$P(B\cup A')+P(A\cap B)=0.73$

Therefore the probability that either B occurs without A occurring or A and B both occur is 0.73.