Question

If A and B are independent events, which equation must be true?

Answer 1

P(B|A) = P(B)

P(B|A) is the conditional probability of B knowing that A is happened. But since A and B are independent events, knowing that A already happened doesn't change anything.

Here's an example: suppose that you have to flip a coin, and then toss a die. A is the event "the coin lands on tails" and B is the event "the die lands with the 5 face up".

Now, we know that B has a probability of 1/6, because each of the six faces of the die will appears with the same probability.

P(B|A) means "what's the probability that the die will land with the 5 face up, knowing that the coin landed on tail?"

Well, it's always 1/6. Knowing that the coin landed on tail changes nothing about the die toss, because the two events are independent.