Question

What is the probability that the total of two dice will be greater than 9, given that the first die is a 5 ?

Answer 1

Let A = first die is 5

Let B = total of two dice is greater than 9

$P\left(A\right)=\frac{1}{6}$

Possible outcomes for A and B : {(5,5), (5,6)}

P(A and B)=$\frac{2}{36}=\frac{1}{18}$

$P\left(B|A\right)=\frac{P(A\cap B)}{P\left(A\right)}$

$=\frac{1}{18}\times 6=\frac{1}{3}$