Conditional Probability

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 given event B.

Front

How do you calculate conditional probability?

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Conditional probability can be 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 and P(B) is the probability of event B.

Front

What does P(A|B) represent?

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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 the condition or event that has already occurred. It normalizes the probability of A given B.

Front

What is the relationship between independent events and conditional probability?

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For independent events, the occurrence of one event does not affect the probability of the other. Therefore, P(A|B) = P(A) for independent events.

Front

If P(A) = 0.5 and P(B) = 0.4, what is P(A and B) if A and B are independent?

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If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

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What is the probability of selecting a female given that the selected person likes a Toyota?

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This is an example of conditional probability, where you would need the total number of females who like Toyotas and the total number of people who like Toyotas to calculate P(Female | Likes Toyota).

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What is the probability of an event that cannot occur?

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The probability of an event that cannot occur is 0%. This is often represented as P(A) = 0.

Front

How do you interpret P(clubs | red) = 0%?

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This means that if the condition is that the item is red, the probability of it being a club is 0%, indicating that no red items are clubs.

Front

What is the total probability rule?

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The total probability rule states that if you have a partition of the sample space, the total probability of an event can be found by summing the probabilities of the event occurring in each partition.