Two fair $6$-sided dice are rolled, one red and one blue. Let $A$ be the event that the red die's result is $3$. Let $B$ be the event that the blue die's result is $4$. Let $C$ be the event that the sum of the rolls is $7$. What is the chance of $\Bbb P(A \mid (B \cap C)')$?
I know the answer is $\frac17$. Could someone show me the process of calculation?
There are 36 equally probable outcomes of the pair of dice. Only one of these is in the event $B\cap C$, namely the one where the red die equals 3 and the blue die equals 4. Of the 35 events remaining in $(B\cap C)'$, exactly 5 of them result in the sum of the two dice equaling 7. Therefore $P(A| (B\cap C)') = \frac5{35} = \frac17$.