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The probabilities of three mutually exclusive events are given by (1+4p)/4, (1-p)/2, and (1-2p)/2. What is the value of p?

1. 1/2
2. 1/3
3. 1/4
4. 2/3

Correct answer: 1/2

Solution

For mutually exclusive events the probabilities must each lie in [0,1] and sum to at most 1. Testing p=1/2: probs are 3/4, 1/4, 0, summing to exactly 1 and all valid. p=1/3 gives a sum of 13/12 > 1, which is impossible. So p = 1/2.

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