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Question

In an exam a student will be qualified if he passes at least two of three test. The probability that he will pass the first test is P. If he fails in one of the test then the probability of his passing in the next test P2 otherwise it is P. The probability of his success follow the polynomial (ap3+bp2+c) then find the value of (a+2b+3c)

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Solution

Probability of success is
=P.P.P+P.P(1P)+P(1P)P2+(1P)P2P
=2p2p3=(1)p3+2p2
According to question
a=1,b=2,c=0a+2b+3c=3

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