<s>[INST] Average number of throws of 2 dice in order for the sum to be a prime number If I throw 2 dice, what's the average number of throws that I need to do in order for the sum of the 2 dice to be a prime number?
My attempt:
The probability that the sum will be a prime number is $\frac{4}{9}$.  And, by applying the formula of mathematical expectation($\frac{1}{p}$) I get $\frac{1}{\frac{4}{9}}$ then $\frac{9}{4} > 1$. Which is not correct.
 [/INST] Prime numbers between $2$ and $12$ are $2,3,5,7,11$
which can be obtained in $15$ ways as $\boxed{1-1}\boxed{ 1-2/2-1}\boxed{1-4/4-1,\; 2-3/3-2}\boxed{1-6/6-1,2-5/5-2,3-4/4-3}\boxed{ 5-6/6-5} $ 
Thus P(prime number) = $\dfrac{15}{36} = \dfrac5{12}$
and $E[X] = 1/p = \dfrac{12}5 = 2.4$
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