APS Practice - Conditional Probability Practice 12-10-24

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.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How do you calculate conditional probability?

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.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for Bayes' Theorem?

Back

Bayes' Theorem is given by: P(A | B) = [P(B | A) * P(A)] / P(B). It allows us to update the probability of A based on new evidence B.

Front

What does it mean if two events are independent?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, P(A | B) = P(A) and P(B | A) = P(B).

Tags

CCSS.HSS.CP.A.3

Front

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

Back

P(2 | number > 3) = 0, because rolling a 2 is impossible if the number is greater than 3.

Tags

CCSS.HSS.CP.B.6

Front

If a box contains 3 blue marbles, 5 red marbles, and 4 white marbles, what is P(blue | not white)?

Back

P(blue | not white) = 3/8, since there are 3 blue marbles and 8 total marbles that are not white.

Tags

CCSS.HSS.CP.B.6

Front

What is the probability of a student having a brother given that they do not have a sister?

Back

P(brother | not sister) = 7/10, based on the given data.

Tags

CCSS.HSS.CP.B.6

Front

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

Back

P(sport | instrument) = 3/14, based on the provided information.

Tags

CCSS.HSS.CP.B.6

Front

What is the probability of drawing an Ace given that the card drawn is a heart?

Back

P(Ace | hearts) = 7.7%, since there is 1 Ace in the 13 hearts.

Tags

CCSS.HSS.CP.B.6

Front

What is the sample space when tossing a die?

Back

The sample space for tossing a die is {1, 2, 3, 4, 5, 6}.