Question

Is it true that p(a|b) = p(b|a) for all events a and b?

Answer 1

No, p(a|b) is not always equal to p(b|a) for all events a and b. However, if events A and B are independent, then p(a|b) = p(a) and p(b|a) = p(b).

Step-by-step explanation:

Independence of Events:

Two events A and B are independent if P(A AND B) = P(A)P(B).

Multiplication Rule:

If A and B are two events, then P(A AND B) = P(B)P(A|B).

In general, p(a|b) is not equal to p(b|a) for all events a and b. However, if events A and B are independent, then p(a|b) = p(a) and p(b|a) = p(b).