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Question

A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are, respectively, p, q and 1/2. if the probability that the student is successful is 1/2, then p(1+q)=

A
12
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B
1
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C
32
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D
34
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Solution

The correct option is B 1
If A,B,C represent events that the student is successful in tests I, II, III, respectively, then the probability that the student is successful is
P[(ABC)(ABC)(ABC)]
=P(ABC)+P(ABC)+P(ABC)
=P(A)P(B)P(C)+P(A)P(B)P(C)+P(A)P(B)P(C)
[A,B,C are independent events]
=pq(112)+p(1q)12+pq12
=pq12pq+12p12pq+12pq
=12(pq+p)
12(pq+p)=12
or p(1+q)=1

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