A test consists of fifteen true/false questions. A student who forgot to study guesses randomly on every question. What is the probability that the student answers exactly five questions correctly?

Guest Mar 22, 2020

#1**+2 **

First, the number of ways to choose 5 questions out of 15 is equivalent to

\(15 \choose 5 \)= \(15!/(10!*5!) = 15*14*13*12*11/(5*4*3*2*1)\)

Canceling out top and bottom, we get:

\(3*7*13*11 = 3003\)

Next, we need the probability that he gets exactly five questions, which is:

\((1/2)^5\)

However, we haven't accounted for the next 10 questions which he needs to get wrong, which is a probability of

\((1/2)^{10}\)

Our answer is then:

\(3003*{1/2}^5*{1/2}^{10} = 3003/(2)^{15}\approx 0.0916442871\)

.jfan17 Mar 22, 2020