Question

There are 6 boxes labeled $B_1,B_2,\dots ..B_6$. In each trial, two fair dice $D_1,D_2$ are known. If $D_1$ shows j and $D_2$ shows k, then j balls are put into the box $B_k$. After n trials, what is the probability that $B_1$ contains at most one ball?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let $P\left(B_1\right)$ be the probability that $B_1$ contains atmost one ball
$P\left(B_1\right)$= $P(B_1$ contains 0 balls) + $P(B_1$ contains 1 balls)
= $P(D_2$ never show 1) + $P(D_2$ shows 1 once when $D_1$ show 1)
$={\left(\frac{5}{6}\right)}^n+\{{}^n{C}_1{\left(\frac{5}{6}\right)}^{n-1}.\frac{1}{6}\}.\frac{1}{6}\Rightarrow D$