Can someone explain why B was the answer ? Thanks.

Problem 39.
Consider two events, A and B. Suppose P(A) = 40% and P(B) = 8%.
The chance that both A and B occur is (select the strongest statement that must be true)
a) at least 40%
b) at most 8% <-- Answer
c) 3.2%
d) at least 8%
e) none of the above is necessarily true

2. ## Re: Probability (help please)

At first glance you might think the answer is (c), since 8% times 40% is 3.2%. But that is true only if P(A) and P(B) are independent, and they don't say whether the events are independent or not. If not then the anwer could be higher than 3.2%. Here's an example of events that aren't independent: if P(A) is the probability of a randomly selected person being female = 50%, and P(B) is the probability of a randomly selected person being a mother = 30%, then the probability that both A and B occur is 30%, not 50% x 30%.

3. ## Re: Probability (help please)

Originally Posted by PennCow
Can someone explain why B was the answer ? Thanks.
Problem 39.
Consider two events, A and B. Supposeq e P(A) = 40% and P(B) = 8%.
The chance that both A and B occur is (select the strongest statement that must be true)
a) at least 40%
b) at most 8% <-- Answer
c) 3.2%
d) at least 8%
e) none of the above is necessarily true
Here is a probability theory answer.
FACT: If for two events, if $U\subseteq V$ then $\mathcal{P}(U)\le \mathcal{P}(V)~.$

Now note that $(A\cap B)\subseteq B~.$