Probability (Multiplication and Addition Rules)

Front

What is the definition of independent events in probability?

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other.

Front

What is the definition of dependent events in probability?

Back

Dependent events are two or more events where the occurrence of one event affects the occurrence of the other.

Front

What is the multiplication rule for independent events?

Back

The probability of both independent events A and B occurring is P(A) * P(B).

Front

What is the addition rule for mutually exclusive events?

Back

The probability of either event A or event B occurring is P(A) + P(B).

Front

What is the addition rule for non-mutually exclusive events?

Back

The probability of either event A or event B occurring is P(A) + P(B) - P(A and B).

Front

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

Back

P(A and B) = P(A) * P(B) = 0.5 * 0.3 = 0.15.

Front

If P(A) = 0.4 and P(B) = 0.6, what is P(A or B) if A and B are mutually exclusive?

Back

P(A or B) = P(A) + P(B) = 0.4 + 0.6 = 1.0.

Front

What is the formula for conditional probability?

Back

P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.

Front

If two events are independent, what is the probability of neither event occurring?

Back

If P(A) and P(B) are the probabilities of events A and B, then the probability of neither occurring is (1 - P(A)) * (1 - P(B)).

Front

What is the probability of rolling a sum of 7 with two dice?

Back

There are 6 combinations to roll a sum of 7 out of 36 total combinations, so P(sum of 7) = 6/36 = 1/6.