Probability Question 280
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 IV. The probabilities of the student passing in tests I, II, III are p, q and $ \frac{1}{2} $ respectively. The probability that the student is successful is $ \frac{1}{2} $ then the relation between p and q is given by
Options:
A) $ pq+p=1 $
B) $ p^{2}+q=1 $
C) $ pq-1=p $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let A, B and C be the events that the student is successful in tests, I, II and III respectively. Then P(The student is successful) $ =P(A)P(B){1-P(C)}+P(A){1-P(B)}P(C)+ $
$ P(A)P(B)P(C) $
$ =p.q( 1-\frac{1}{2} )+p(1-q)\frac{1}{2}+p.q\frac{1}{2} $
$ =\frac{1}{2}pq+\frac{1}{2}p(1-q)+\frac{1}{2}pq $
$ =\frac{1}{2}(pq+p-pq+pq)=\frac{1}{2}(pq+p) $
$ \therefore \frac{1}{2}=\frac{1}{2}(pq+p)\Rightarrow 1=pq+p $
BETA
