Question

True or False: Events A and B are independent. ()=25 P ( A ) = 2 5 ()=14 P ( B ) = 1 4 (()=125

Answer 1

Events A and B are not independent because the condition P(A and B) = P(A) * P(B) is not satisfied.

Step-by-step explanation:

True or False: Events A and B are independent.

Two events, A and B, are independent if the following conditions are met:

1. P(A and B) = P(A) * P(B)
2. P(B|A) = P(B)

In this question, we are given:

P(A) = 2/5

P(B) = 1/4

P(A and B) = 1/25

To check if events A and B are independent, we can substitute the given values into the conditions for independence.

1. P(A and B) = P(A) * P(B) = (2/5) * (1/4) = 2/20 = 1/10 ≠ 1/25
2. P(B|A) = P(B)

Since the first condition is not satisfied, events A and B are not independent. Therefore, the statement is false.