MCQ

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There are $6$ boxes labelled $B_1, B_2, \ldots, B_6$. In each trial, two fair dice $D_1, D_2$ are thrown. 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
  $\left(\frac{5^{n-1}}{6^{n-1}}\right)+\left(\frac{5^n}{6^n}\right)\left(\frac{1}{6}\right)$
• B
  $\left(\frac{5^n}{6^n}\right)+\left(\frac{5^{n-1}}{6^{n-1}}\right)\left(\frac{1}{6}\right)$
• C
  $\left(\frac{5^n}{6^n}\right)+n\left(\frac{5^{n-1}}{6^{n-1}}\right)\left(\frac{1}{6}\right)$
• ✓
  $\left(\frac{5^n}{6^n}\right)+n\left(\frac{5^{n-1}}{6^{n-1}}\right)\left(\frac{1}{6^2}\right)$