A student appears for test I and II. The student is successful if he passes either in test I or test II. The probability of the student passing in test I and II are p and `1/3` respectively. If the probability that the student is successful is `1/2` then find the value of p.

Options

A. `1//2`
B. 1
C. `3//2`
D. `3//4`

Explanation

If A,B, C represent events that the student is successful in tests `I,II,III,` respectively, the the proability that the student is successful is
`P[AnnB nnC')uu(AnnB'C')uu(AnnBnnC)]`
`=P(AnnBnnC')+P(AnnB'nnC)+P(AnnBnnC)`
`=P(A)P(B)P(C')+P(A)P(B')P(C')+P(A)P(B)P(C)`
`" "[thereforeA,B,C "are independent events"]`
`=pq(1-(1)/(2))+p(1-q)1/2+pq1/2`
`=pq+1/2p-1/2pq`
`=1/2(pq+p)`
`therefore1/2(pq+q)=1/2`
`orp(1+q)=1`