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 given event B.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How do you calculate conditional probability?

Back

Conditional probability can be 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.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(A|B) represent?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the significance of the denominator in the conditional probability formula?

Back

The denominator, P(B), represents the probability of the condition or event that has already occurred. It normalizes the probability of A given B.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the relationship between independent events and conditional probability?

Back

For independent events, the occurrence of one event does not affect the probability of the other. Therefore, P(A|B) = P(A) for independent events.

Tags

CCSS.HSS.CP.A.3

Front

If P(A) = 0.5 and P(B) = 0.4, what is P(A and B) if A and B are independent?

Back

If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the probability of selecting a female given that the selected person likes a Toyota?

Back

This is an example of conditional probability, where you would need the total number of females who like Toyotas and the total number of people who like Toyotas to calculate P(Female | Likes Toyota).

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the probability of an event that cannot occur?

Back

The probability of an event that cannot occur is 0%. This is often represented as P(A) = 0.

Tags

CCSS.7.SP.C.5

Front

How do you interpret P(clubs | red) = 0%?

Back

This means that if the condition is that the item is red, the probability of it being a club is 0%, indicating that no red items are clubs.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the total probability rule?

Back

The total probability rule states that if you have a partition of the sample space, the total probability of an event can be found by summing the probabilities of the event occurring in each partition.