Question

Select the correct answer. 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 P(A) y

Answer 1

P(A) = probability of event A, P(B) = probability of event B

P(A) = x is given to us

P(B) = y is also given

--------------------------

If A and B are independent, then neither event affects the other. If we know A happens, then that doesn't change the probability of B happening (vice versa).

So that means P(A|B) = P(A) = x and P(B|A) = P(B) = y

This points to the answer being P(B|A) = y which is choice A or the first answer choice

note: P(A|B) is read as "probability of A given that B has happened". It is known as conditional probability. The symbol between the A and B is not the letter i or L, it is a vertical pipe symbol to separate the letters.