M107_U2_H29_Conditional Probability

Front

What is Conditional Probability?

Back

Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of A given B.

Front

How is Conditional Probability calculated?

Back

P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both A and B occurring.

Front

What does P(A ∩ B) represent?

Back

P(A ∩ B) represents the probability that both events A and B occur simultaneously.

Front

What is the formula for the Union of Two Events?

Back

P(A ∪ B) = P(A) + P(B) - P(A ∩ B), which calculates the probability that either event A or event B occurs.

Front

If P(A) = 0.7 and P(B) = 0.5, what is P(A ∩ B) if P(A ∪ B) = 1?

Back

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.7 + 0.5 - 1 = 0.2.

Front

What is the Complement Rule in probability?

Back

The Complement Rule states that the probability of an event not occurring is 1 minus the probability of the event occurring: P(A') = 1 - P(A).

Front

What is the meaning of P(B|A)?

Back

P(B|A) is the probability of event B occurring given that event A has occurred.

Front

How do you interpret P(A|B) = 0.4?

Back

This means that if event B occurs, there is a 40% chance that event A will also occur.

Front

What is Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events: P(A|B) = [P(B|A) * P(A)] / P(B).

Front

If P(A) = 0.3 and P(B|A) = 0.5, what is P(A ∩ B)?

Back

P(A ∩ B) = P(A) * P(B|A) = 0.3 * 0.5 = 0.15.