If A and B are disjoint with P(A) = 0.3 and P(B) = 0.25, what is P(A ∪ B)?

If A and B are disjoint with P(A) = 0.3 and P(B) = 0.25, what is P(A ∪ B)?

• A. 0.55
• B. 0.10
• C. 0.75
• D. 0.30

Answer: (A)

When two events cannot happen at the same time, the probability of either one occurring is the sum of their probabilities. This is because there’s no overlap to subtract. In that case, P(A ∪ B) = P(A) + P(B). Here, P(A) = 0.3 and P(B) = 0.25, so P(A ∪ B) = 0.3 + 0.25 = 0.55. Since they are disjoint, there’s no intersection to subtract, which is why the union probability is simply the sum. The other numbers would require either overlap between A and B or a different setup, which isn’t the case here.

When two events cannot happen at the same time, the probability of either one occurring is the sum of their probabilities. This is because there’s no overlap to subtract. In that case, P(A ∪ B) = P(A) + P(B).

Here, P(A) = 0.3 and P(B) = 0.25, so P(A ∪ B) = 0.3 + 0.25 = 0.55. Since they are disjoint, there’s no intersection to subtract, which is why the union probability is simply the sum.

The other numbers would require either overlap between A and B or a different setup, which isn’t the case here.