Hello ibetan Originally Posted by

**ibetan** Thanks. I understand everything you did except the part in $\displaystyle 3(0.7667)^2$ , why did you multiply by 3?

This is an example of the Binomial Distribution Formula. The probability of getting $\displaystyle r$ successes from $\displaystyle n$ trials is:$\displaystyle \binom nrp^r(1-p)^{n-r}$

Here, $\displaystyle p = 0.7667, \;n = 3,\; r = 2$. The probability of getting 2 questions right out of 3 is:

$\displaystyle \binom 32(0.7667)^2(1-0.7667)^1$

and $\displaystyle \binom32 = 3$. This is where the 3 comes from.

It is simply the number of ways of choosing 2 questions out of 3, these being the questions that Aki gets right. He could get:

right, right, wrong

or

right, wrong, right

or

wrong, right, right

3 ways. Do you see now?

Grandad