Question

If we toss two balanced dice, and let A be the event that the sum of the face values

of two dice is 8, and B be the event that the face value of the first one is 3. Calculate

P(A/B).

Answer 1

$A=\{(2,6),(3,5),(4,4),(5,3),(6,2)\},\\ B=\{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\},\\ A\cap B=\{(3,5)\}-\text{both the events A and B} \\\text{happened simultaneously.}$

Let's use the conditional probability formula:

$P(A|B)=\cfrac{P(A\cap B)}{P(B)}.$

Total number of outcomes for a toss of two dice is $n=6\cdot6=36.$

So,

$P(A\cap B)=\cfrac{1}{36},\\ P(B)=\cfrac{6}{36},\\ P(A|B)=\cfrac{1/36}{6/36}=\cfrac{1}{6}.$