Probability

**shogunhd** · February 5th 2008, 04:16 PM

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

**Soroban** · February 5th 2008, 05:24 PM

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: . $\begin{array}{ccc} P(\text{right}) &=& \frac{1}{5} \\ P(\text{wrong}) &=&\frac{4}{5}\end{array}$

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

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

b) being correct on two questions only

There are: . ${6\choose 2} \:=\:15$ ways to choose two questions.

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

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