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Question

A student appears for tests I,II and III. The student is successful only if he passes either in tests I and II or tests I and III(not all the 3).
The probabilities of the student passing in tests I,II,III are p,q and 13 respectively. The probability that the student is successful is 16 and the relation between p and q is 1k=pq+p. Then the value of k is:

A
2
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B
2.0
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C
2.00
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Solution

Probability that the student is successful =16
= Probability that student passes only in tests I & II or tests I & III =P(I)P(II)P(III)+P(I)P(II)P(III)=(p)(q)(23)+(p)(1q)(13)=pq3+p3
16=pq3+p312=pq+p
Since, 1k=pq+p
Hence, k=2

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