Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred.

Front

How is Conditional Probability calculated?

Back

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

Front

What does P(A | B) represent?

Back

The probability of event A occurring given that event B has occurred.

Front

If P(A) = 1/2 and P(B) = 1/3, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6.

Front

What is the formula for the total probability theorem?

Back

P(A) = Σ P(A | B_i) * P(B_i) for all i, where B_i are mutually exclusive events.

Front

What is the complement rule in probability?

Back

P(A') = 1 - P(A), where A' is the complement of event A.

Front

What is the probability of rolling an even number on a fair die?

Back

P(even) = 3/6 = 1/2.

Front

What is the probability of rolling a number less than 5 given that the number is even?

Back

P(less than 5 | even) = 2/3.

Front

What is the probability of rolling a 2 given that the number rolled is greater than 3?

Back

P(2 | greater than 3) = 0.

Front

What is the probability of a student playing a sport given they play an instrument?

Back

P(sport | instrument) = 3/14.