Question

If the probability of one event occurring is .40 and the probability of a second event occurring is 0.60, then the probability that both events will occur must be 1.0 since that is the maximum value a probability can be. select one:
a. True
b. False

Answer 1

Let $P(A)=0.4$ and $P(B)=0.6$. The the probability both events occurring $P(AB)=P(A)P(B|A)=P(B)P(A|B)$.

This shows $P(AB) \leq \min(P(A),P(B)) \\ P(AB) \leq \min(0.4,0.6)\\ P(AB) \leq 0.4$

If A and B are independent

$P(AB)=P(A)P(B)=0.4*0.6=0.24$

Thus, the statement is (B) False.