1. ## Bernoulli/Binomial Distributions

There is this one part of a problem I'm having trouble setting up...

On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of
For this, I let $\displaystyle X=1$ if answer is correct, and $\displaystyle X=0$ if the answer is incorrect.

(a) Being correct only on questions 1 and 4 (i.e. C, I, I, C, I, I)
I'm not quite sure on how to set this part up, any hints would be appreciated.

(b) Being correct on two questions
I think this would be $\displaystyle P\left(X=2\right)=\binom62\left(\frac{1}{5}\right) ^2\left(\frac{4}{5}\right)^4$...but I'm not quite sure.

I'd appreciate any input!

--Chris

2. Originally Posted by Chris L T521
There is this one part of a problem I'm having trouble setting up...

On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of

(a) Being correct only on questions 1 and 4 (i.e. C, I, I, C, I, I)

For this, I let $\displaystyle X=1$ if answer is correct, and $\displaystyle X=0$ if the answer is incorrect.

I'm not quite sure on how to set this part up, any hints would be appreciated.

(b) Being correct on two questions
I think this would be $\displaystyle P\left(X=2\right)=\binom62\left(\frac{1}{5}\right) ^2\left(\frac{4}{5}\right)^4$...but I'm not quite sure.

I'd appreciate any input!

--Chris
(b) is correct.

For (a), it's simply $\displaystyle \left( \frac{1}{5}\right) \, \left( \frac{4}{5}\right)^2 \, \left( \frac{1}{5}\right) \, \left( \frac{4}{5}\right)^2 = \left( \frac{1}{5}\right)^2 \, \left( \frac{4}{5}\right)^4$.