The probability for event cap A is 0 point 4 , the probability for event cap b is 0 point 2 , and the probability of events cap A and cap b is 0 point 1 Why are the events not independent?
Answer
A
The sum of cap p times cap A and cap p times cap b is greater than cap p times open paren cap A and cap b close paren .
B
The sum of cap p times cap A and cap p times cap b is not equal to cap p times open paren cap A and cap b close paren .
C
The product of cap p times cap A and cap p times cap b is greater than cap p times open paren cap A and cap b close paren .
D
The product of cap p times cap A and cap p times cap b is not equal to cap p times open paren cap A and cap b close paren .
Explanation
For independent events, the probability that both occur must equal the product of their individual probabilities: P(A and B) = P(A) × P(B). Here, 0.4 × 0.2 = 0.08, but P(A and B) is 0.1. Since the product does not equal the probability of both events, the events are not independent. Choice B states this condition.
AI-written and checked against the verified answer.