A) \[pq+p=1\]
B) \[{{p}^{2}}+q=1\]
C) \[pq-1=p\]
D) None of these
Correct Answer: A
Solution :
[a] 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) \[=P(A)P(B)\{1-P(C)\}+P(A)\{1-P(B)\}P(C)+\]\[P(A)P(B)P(C)\] \[=p.q\left( 1-\frac{1}{2} \right)+p(1-q)\frac{1}{2}+p.q\frac{1}{2}\] \[=\frac{1}{2}pq+\frac{1}{2}p(1-q)+\frac{1}{2}pq\] \[=\frac{1}{2}(pq+p-pq+pq)=\frac{1}{2}(pq+p)\] \[\therefore \frac{1}{2}=\frac{1}{2}(pq+p)\Rightarrow 1=pq+p\]You need to login to perform this action.
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