# Math Help - Challenging probability question

1. ## Challenging probability question

The probability that a student passes an exam is 1/3. If 5 people took the exam, what is the probability that only 4 of them pass?

A. (1/3)^5
B. 4(2/3)^4 * 4(1/3)
C. 4(1/3)^4 * (2/3)
D. (2/3)^5
E. 5(1/3)^4 * (2/3)
F. None of the above

Can someone post up what the answer is and an explanation for this?

2. I assume you mean EXACTLY 4 of 5.
This is a binomial rv with n=5 and p=1/3... ${5\choose 4} \biggl({1\over 3}\biggr)^4 \biggl({2\over 3}\biggr)^1$.
So, E is correct.