Question

Events A and B are independent. Suppose event A occurs with probability 0.96 and event B occurs with probability 0.62.

a. Compute the probability that A occurs but B does not occur.

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

Answer 1

If A and B are independent events then $P(A \cap B)=P(A)*P(B)$

a) the probability that A occurs but B does not = $P(A \cap B^c)= P(A)*P(B^c)=0.96*(1-0.62)=0.3648$

b) The probability that either A occur without B occuring or A and B both occur

The probability that A and B both occur $P(A \cap B)=P(A)P(B)=0.96*0.62=0.5952$

The probability that either A occur without B occuring or A and B both occur is $P(A \cap B^c)+P(A \cap B)=0.96$