(12/04 & 05) CRM Unit 3: Conditional Probability Practice

Front

What is the definition of 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.

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.

Front

What is the probability of rolling a 5 on a regular 6-sided die?

Back

The probability of rolling a 5 on a regular 6-sided die is P(5) = 1/6.

Front

What does P(A|B) represent in probability?

Back

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

Front

If P(A) = 0.3 and P(B) = 0.5, what is P(A and B) if A and B are independent?

Back

If A and B are independent, then P(A and B) = P(A) * P(B) = 0.3 * 0.5 = 0.15.

Front

What is the formula for the total probability theorem?

Back

The total probability theorem states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

Front

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

Back

The probability that a student plays sports given that they do community service is P(plays sports | does community service) = 5/15.

Front

What is the probability that a student does not play an instrument given they play a sport?

Back

This is calculated using conditional probability: P(does not play instrument | plays sport).

Front

What is the probability of event A if P(A) = 0.4 and P(B) = 0.6, and A and B are mutually exclusive?

Back

If A and B are mutually exclusive, then P(A or B) = P(A) + P(B) = 0.4 + 0.6 = 1.

Front

What is the probability that a student is male given they are full-time?

Back

The probability that a student is male given they are full-time is P(Male | Full Time) = 3/10.