Conditional Probability Practice

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

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

What is the significance of the denominator in the Conditional Probability formula?

Back

The denominator P(B) represents the probability of event B occurring, which serves as the condition for the probability of event A.

Front

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

Back

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

Front

What is the probability that a student plays sports given that they do community service?

Back

P(Sports | Community Service) = \frac{5}{15}.

Front

What is the probability that a female is chosen given they like a Toyota?

Back

P(Female | Likes Toyota) = 0.6774.

Front

How do you interpret P(Part Time | Female)?

Back

P(Part Time | Female) represents the probability that a student is part-time given that the student is female.

Front

What is the probability of selecting an odd number given that the number is less than 7 from the set {1, 2, 3, 4, 5, 6, 7, 8}?

Back

P(Odd | Less than 7) = \frac{3}{6} = \frac{1}{2}.

Front

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

Back

P(2 | Number > 3) = 0.