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X and Y are two random independent events. It is known that P(X) = 0.4 and P(X ∪ Y^c) = 0.7. Which one of the following is the value of P(X ∪ Y)?

1. 0.7
2. 0.5
3. 0.4
4. 0.3

Correct answer: 0.7

Solution

With independence, 0.7=0.4+(1-p)-0.4(1-p)=0.4+0.6(1-p), giving 1-p=0.5 so P(Y)=0.5. Then P(X u Y)=0.4+0.5-0.4*0.5=0.7. Stored answer 0.5 is wrong; correct is 0.7.

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