Question

If P(A) = 1/2 and P(A ∩ B) = 1/5, for A and B to be independent, what should P(B) be?

a) 1/10
b) 4/10
c) 3/10
d) 7/10

Answer 1

For events A and B to be independent with P(A) = 1/2 and P(A ∩ B) = 1/5, P(B) must be 2/5 or 4/10, which corresponds to option b.

Step-by-step explanation:

To determine the probability of event B for events A and B to be independent events, we use the definition of independent events: two events A and B are independent if and only if P(A ∩ B) = P(A)P(B). We're given that P(A) = 1/2 and P(A ∩ B) = 1/5. To find P(B), we set up the equation based on the rule of independence and solve for P(B).

Using the equation:

P(A ∩ B) = P(A)P(B),
1/5 = (1/2)P(B),
P(B) = (1/5) / (1/2),
P(B) = 2/5 or 4/10.

Therefore, for events A and B to be independent, P(B) must be 4/10, which is option b.