Combined Probability

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What is Combined Probability?

Back

Combined probability refers to the probability of two or more events happening at the same time. It can be calculated using the addition rule for mutually exclusive events or the multiplication rule for independent events.

Front

Define the Addition Rule in Probability.

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The Addition Rule states that the probability of the occurrence of at least one of two events is the sum of their individual probabilities minus the probability of their intersection: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the Multiplication Rule in Probability?

Back

The Multiplication Rule states that the probability of the occurrence of two independent events is the product of their individual probabilities: P(A and B) = P(A) * P(B).

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How do you calculate the probability of an event not occurring?

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The probability of an event not occurring is calculated as: P(not A) = 1 - P(A).

Front

What is a sample space in probability?

Back

A sample space is the set of all possible outcomes of a probability experiment.

Front

Explain what a complementary event is.

Back

A complementary event is the event that represents all outcomes in the sample space that are not included in the event itself. For event A, the complement is denoted as A'.

Front

What does it mean for two events to be independent?

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Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Front

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

Back

The probability of rolling a sum of 7 with two dice is calculated by finding the number of favorable outcomes (6) divided by the total outcomes (36): P(sum of 7) = 6/36 = 1/6.

Front

How do you find the probability of 'A or B' when A and B are not mutually exclusive?

Back

When A and B are not mutually exclusive, use the formula: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the formula for conditional probability?

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The formula for conditional probability is: P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.