147k views
1 vote
If A and B are independent events, which equation must be true?

A. P(B|A) = P(A)
B. P(B|A) = P(B)
C. P(B|A) = P(A) × P(B)
D. P(B|A) = P(A) + P(B)

User Ursa Major
by
7.8k points

2 Answers

3 votes

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.

User Linus Caldwell
by
8.1k points
2 votes

Answer:

B. P(B|A) = P(B)

Explanation:

For all Plato users

User Obaydur Rahman
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories