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 event A occurring given that event B has occurred.

Front

How is Conditional Probability calculated?

Back

Conditional Probability is calculated using the formula: P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring and P(B) is the probability of event B.

Front

What does P(A|B) represent?

Back

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

Front

If P(A) = 0.4 and P(B) = 0.5, what is P(A|B) if P(A and B) = 0.2?

Back

P(A|B) = P(A and B) / P(B) = 0.2 / 0.5 = 0.4.

Front

What is the relationship between independent events and Conditional Probability?

Back

For independent events, P(A|B) = P(A). This means the occurrence of event B does not affect the probability of event A.

Front

What is the probability of event A if P(A|B) = 0.6 and P(B) = 0.5?

Back

To find P(A), you need P(A and B). If P(A|B) = 0.6, then P(A and B) = P(A|B) * P(B) = 0.6 * 0.5 = 0.3.

Front

What is the complement of an event?

Back

The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is given by P(A') = 1 - P(A).

Front

If P(A) = 0.3, what is P(A')?

Back

P(A') = 1 - P(A) = 1 - 0.3 = 0.7.

Front

What is the formula for finding the probability of two independent events A and B occurring together?

Back

For independent events, P(A and B) = P(A) * P(B).

Front

What is the probability of rolling a 3 on a fair die?

Back

The probability of rolling a 3 on a fair die is P(3) = 1/6.