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 $\frac{P}{2}$ otherwise it is ${}^{\prime }{P}^{\prime }$. The probability of his success follow the polynomial $(a{p}^3+b{p}^2+c)$ then find the value of $(a+2b+3c)$

Answer 1

Probability of success is
$=P.P.P+P.P(1-P)+P(1-P)\frac{P}{2}+(1-P)\frac{P}{2}P$
$=2p^2-p^3=(-1)p^3+2p^2$
According to question
$a=-1,b=2,c=0\Rightarrow a+2b+3c=3$