Question

If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) a. is 1.00. b. is 0.5. c. is 0.00. d. None of these alternatives are correct.

Answer 1

The answer is (d) "None of the these alternatives are correct"

Explanation:

If two events A and B are independent, the probability of the intersection
`P(A\cap B)` is defined as:

`P(A\cap B)=P(A)\cdot P(B)`

Therefore, in the exercise:

`P(A\cap B)=P(A)\cdot P(B)=0.5\cdot 0.5\\P(A\cap B)=0.25`

which give (d) "None of the these alternatives are correct"