Question

Marti rolls two dice what is the probability that the sum of the dice is 7 given that the first die is 2

Answer 1

A - the sum of two dice is 7

B - the first die is 2

$P(A|B)=\dfrac{P(A \cap B)}{P(B)}\\\\ |\Omega|=6^2=36\\ |A\cap B|=1\\ |B|=1\cdot6=6\\\\ P(A\cap B)=\dfrac{1}{36}\\ P(B)=\dfrac{6}{36}=\dfrac{1}{6}\\\\ P(A|B)=\dfrac{\dfrac{1}{36}}{\dfrac{1}{6}}=\dfrac{1}{36}\cdot6=\dfrac{1}{6}$

Answer 2

We have 6x6 for all the possibilities for rolling 2 dices. and we know: (2;5) is the only way So the answer should be 1/36 i hope its right  :)