For this question only, we suppose that the event that Supplier A delivers in 4 days and the event that Supplier B delivers in 4 days are no longer independent, and we assume that these events are mutually exclusive. What is the probability that at least one supplier delivers the material in 4 days?

(Hint: If two events are mutually exclusive, what is the probability that both events will happen?)

Question

For this question only, we suppose that the event that Supplier A delivers in 4 days and the event that Supplier B delivers in 4 days are no longer independent, and we assume that these events are mutually exclusive. What is the probability that at least one supplier delivers the material in 4 days?

(Hint: If two events are mutually exclusive, what is the probability that both events will happen?)

BlackTom AI · Accepted Answer

We start by restating the core setup: we are told that the event 'Supplier A delivers in 4 days' and the event 'Supplier B delivers in 4 days' are mutually exclusive. This means that both events cannot happen at the same time.

Under mutual exclusivity, the probability that at least one of the events occurs is the sum of their individual probabilities: P(A or B) = P(A) + P(B).

Because the events cannot both occur, we do not subtract the intersection term (which would be needed if we were dealing with independence or general overlap). Therefore, the joint probability is simply the additive combination of the two probabilities.

If the provided answer is 0.9000, this implies that the individual probabilities must sum to 0.9000, i.e., P(A) + P(B) = 0.9. For example, possible combinations could be P(A) = 0.45 and P(B) = 0.45, or P(A) = 0.60 and P(B) = 0.30, etc., as long as their sum equals 0.9.

Compare this to the common alternative scenario (where the events might be independent): if A and B were independent, P(A or B) would be P(A) + P(B) - P(A)P(B), which would generally yield a different result. The mutual exclusivity condition removes the P(A)P(B) intersection term entirely, simplifying the calculation to a straight sum.

Key insight: the mutual exclusivity assumption directly determines the calculation pathway. The total probability of at least one delivery in 4 days is exactly the sum of the two individual delivery probabilities, with no overlap to subtract.

If you’re given only the final numeric result 0.9000, you can verify consistency by checking that the sum of the two individual delivery probabilities equals 0.9. If any additional context provided values for P(A) or P(B), you would simply add them to confirm the total probability.

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