The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests?
A
\(\frac{2}{27}\)
B
\(\frac{3}{27}\)
C
\(\frac{4}{27}\)
D
\(\frac{5}{3}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Pass(P) = \(\frac{2}{3}\), Fail(F) = \(\frac{1}{3}\)
T = P.P.F ==> \(\frac{2}{3} \times \frac{2}{3} \times \frac{1}{3}\) = \(\frac{4}{27}\)
Source: Myschool Past Questions Archive (Record #27397)