Question

Suppose that P (A)=0.4 AND P (B)=0.2, If events A & B ARE Mutually EXCLUSIVE :

- What is the probability of either A or B occurring
- What is the probability of neither A nor B will happen

Answer 1

Part (a) Finding the probability of either A or B

We are told that events A and B are mutually exclusive. This means they cannot happen at the same time. We can say P(A and B) = 0

Furthermore,

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.4 + 0.2 - 0

P(A or B) = 0.6

Answer: 0.6

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Part (b) Finding the probability of neither A nor B

P(A or B) + P(neither A nor B) = 1

P(neither A nor B) = 1 - P(A or B)

P(neither A nor B) = 1 - 0.6

P(neither A nor B) = 0.4

The reason why this works is to imagine throwing a dart at the Venn diagram. You'll either...

• you land in A or B (pick one but not both), OR,
• you'll land outside both regions A and B.

One or the other must happen. Both events cannot happen simultaneously.

Answer: 0.4