The probability of a student passing any exam is 2/3. If the student takes three exams, what is the probability that he will not pass any of them?
A
2/3
B
4/9
C
8/27
D
1/27
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
P(not passing exam) = \(1 - \frac{2}{3} = \frac{1}{3}\)
P(not passing any of the three exams) = \(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\)
= \(\frac{1}{27}\)
Source: Myschool Past Questions Archive (Record #3388)