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Prabh Dhaliwalsays

I understand that when doing probability that A or B occurs you add probabilities but in some scenarios you must subtract the probably that both A and B occur from the sum. Which scenarios does this apply to.

When events A and B are mutually exclusive, meaning events that cannot occur at the same time, we have P(A and B)=0. For example, if a 6-sided die is rolled once, the event of rolling an odd number and the event of rolling an even number are mutually exclusive. In this case, the formula reduces to P(A or B, or both, occur) = P(A) + P(B). But you are right that in the general case P(A or B, or both, occur) = P(A) + P(B) – P(both A and B occur), which then reduces to the sum of the probabilities of the two events when they are mutually exclusive.

Prabh Dhaliwal says

I understand that when doing probability that A or B occurs you add probabilities but in some scenarios you must subtract the probably that both A and B occur from the sum. Which scenarios does this apply to.

P(AUB)= P(A) + P(B) – P(A and B)

Dabral says

When events A and B are mutually exclusive, meaning events that cannot occur at the same time, we have P(A and B)=0. For example, if a 6-sided die is rolled once, the event of rolling an odd number and the event of rolling an even number are mutually exclusive. In this case, the formula reduces to P(A or B, or both, occur) = P(A) + P(B). But you are right that in the general case P(A or B, or both, occur) = P(A) + P(B) – P(both A and B occur), which then reduces to the sum of the probabilities of the two events when they are mutually exclusive.