Question

For the following statement, determine if it is true or false. If events A and B are known to be independent and P(A) = 0.2 and P(B) = 0.3, then P(A and B) = 0.5. A) True B) False

Answer 1

The statement is False.

When events A and B are known to be independent, the probability of both events occurring together, denoted as P(A and B), is equal to the product of their individual probabilities, P(A) and P(B).

In this case, P(A) = 0.2 and P(B) = 0.3. To find P(A and B), we multiply these probabilities:

P(A and B) = P(A) * P(B) = 0.2 * 0.3 = 0.06

Therefore, P(A and B) is equal to 0.06, not 0.5. Thus, the statement "P(A and B) = 0.5" is False.

It is important to note that the probability of two independent events occurring together is generally less than the individual probabilities of each event.