Q.
Let $D_1, D_2, D_3$ be three tetrahedral dice where $D_1, D_2$ are printed with digits $3,3,4,6$ and $D_3$ is printed with $1,1,2,3$ on their faces. On throwing a dice each face is equally likely to fall. Outcome of the dice is the number appearing on the face which is downwards after the thrown. If $A$ and $B$ tosses a biased coin $\left( P ( H )=\frac{1}{3}\right)$ alternately starting with $A$. If $A$ throws tail before $B$ throws head then A wins the toss, they continue toss indefinitely, until one of them wins the toss. Now the winner randomly select 2 dice and rolled once. Three events $A , B$ and $E$ are defined as
A: 'A' wins the toss;
$B :$ ' $B$ ' wins the toss
$E :$ Sum on the dice is divisible by 3 .
$P \left(\frac{ B }{ E }\right)$ is equal to
Probability - Part 2
Solution: