1. ## Probability

Hi

The question is:

On a six question multiple choice test there are five possible answers for each question. Only one of these answers is correct. If a student guesses randomly and independently, find the probability:

a) being correct only on questions 1 and 4
b) being correct on two questions only

2. Hello,shogunhd!

On a six-question multiple-choice test, there are five possible answers
for each question. Only one of these answers is correct.
If a student guesses randomly and independently, find the probability:

a) being correct only on questions 1 and 4
On any question: .$\displaystyle \begin{array}{ccc} P(\text{right}) &=& \frac{1}{5} \\ P(\text{wrong}) &=&\frac{4}{5}\end{array}$

We want: .right-wrong-wrong-right-wrong-wrong

The probability is: .$\displaystyle \frac{1}{5}\cdot\frac{4}{5}\cdot\frac{4}{5}\cdot\f rac{1}{5}\cdot\frac{4}{5}\cdot\frac{4}{5} \;=\;\frac{256}{15.625}$

b) being correct on two questions only
There are: .$\displaystyle {6\choose 2} \:=\:15$ ways to choose two questions.

$\displaystyle P(\text{2 right}) \;=\;15\cdot\left(\frac{1}{5}\right)^2\left(\frac{ 4}{5}\right)^4 \;=\;\frac{768}{3125}$