Question 1116434
<br>
The probability that 9 of 18 students pass, if the probability of passing is p and the probability of failing is (1-p), is<br>
{{{C(18,9)p^9(1-p)^9}}}<br>
So we have<br>
{{{C(18,9)p^9(1-p)^9 = .0642543198}}}
{{{p^9(1-p)^9 = 1.321561493*10^-6}}}
{{{p(1-p) = (1.321561493*10^-6)^(1/9) = 2/9}}}<br>
This is more easily solved by inspection than by formal algebra: p = 2/3, 1-p = 1/3.<br>
Answer: The probability of passing the exam is 2/3.