What is the Probability of A' n B' Given A' and A, B, and A n B?

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In summary, conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the two events occurring together by the probability of the first event occurring. The difference between joint probability and conditional probability is that joint probability is the likelihood of two events occurring together, while conditional probability takes into account the occurrence of one event before calculating the probability of another event. Conditional probability should be used when the probability of an event is dependent on the occurrence of another event. It can never be greater than 1 as it represents a likelihood and must fall between 0 and 1.
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hellokitten
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Given P(A), P(B), and P(A n B) . Find the P(A' n B' | A')
We know P(AuB) = P(A)+P(B)- P(A n B)
Then
P(A' n B'|A') = P(A' n B' n A' ) / P(A') = P(A' n B') / P(A') = P(A u B)' /P(A') = [1-P(A u B) ]/ P(A') =
[1-P(A u B)] / [1-P(A)] Correct?
 
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FAQ: What is the Probability of A' n B' Given A' and A, B, and A n B?

What is the definition of conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred.

How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the two events occurring together by the probability of the first event occurring.

What is the difference between joint probability and conditional probability?

Joint probability is the likelihood of two events occurring together, while conditional probability takes into account the occurrence of one event before calculating the probability of another event.

When should conditional probability be used?

Conditional probability should be used when the probability of an event is dependent on the occurrence of another event.

Can conditional probability be greater than 1?

No, conditional probability can never be greater than 1 as it represents a likelihood and must fall between 0 and 1.

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