For a student to qualify, he must pass at least two our three exams. The probability that he will pass the first exam is p. If he fails in one of the exams then the probability of his passing in the next is p/2, otherwise it remains the same. Find the probability that he will qualify.

Answer

B, C

Explanation

Let `E_(i)` denotes the event that the students will pass the ith exam, where `i=1,2,3`
and E denotes the student will qualify.
`:." "P(E)=[P(E_(1))xxP(E_(2)//E_(1))]+[P(E_(1))xxP(E_(2)'//E_(1))xxP(E_(3)//E_(2)')]+[P(E_(1)')xxP(E_(2)//E'_(1))xxP(E_(3)//E_(2))]`
`=p^(2)+p(1-p).(p)/(2)+(1-p).(p)/(2).p`
`implies" "P(E)=(2p^(2)+p^(2)-p^(3)+p^(2)-p^(3))/(2)=2p^(2)-p^(3)`