Question

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?

A) P(B|A) = y
B) P(A|B) = y
C) P(B|A) = x
D) P(A and B) = x + y
E) P(A and B) = x * y

Answer 1

For two events A and B to be independent, the joint probability must be the product of their individual probabilities. The correct condition is E) P(A AND B) = x * y.

Step-by-step explanation:

The student asked which condition must be true if two events, event A with probability x and event B with probability y, are independent. For two events to be independent, the conditional probabilities must equal the original probabilities, and the joint probability equals the product of their individual probabilities.

Conditions for Independent Events

• P(A AND B) = P(A) \u2219 P(B)
• P(B|A) = P(B)
• P(A|B) = P(A)

Given the options, E) P(A AND B) = x * y is the correct condition that demonstrates the independence of events A and B. Since the events are independent, the joint probability of both events occurring is the product of their individual probabilities: P(A) \u2219 P(B).