Originally Posted by

**Plato** This is a poorly written question. In #1 it should say if one die is rolled or a pair of dice taking the sum.

In one reply you are told that your solution for #2 is correct. I disagree .

You have correctly understood that there are only thirty pairs with different faces.

However. there are **ten pairs** that contain a four:

$(4,1),~(4,2),~(4,3),~(4,5),~(4,6),~(6,4)~,(5,4)~, (3,4)~,(2,4)~,(1,4)$

So what is the correct answer for #2?

For #3. BTW. a couple of engineering professors at a CalState have proven that if a coin is filliped and caught on the fly, it is impossible for it to be unfair.

We of course can design an experiment that mimics this question.

Let $X$ be the number of heads in three tosses, $X=0,1,2,3$.

$\mathcal{P}(X=n)=\dbinom{3}{n}(1/4)^n(3/4)^{3-n}$