Solutions - 5030-03

(1) Set up the conditional probability formula:

P [D_{1} = 1 \cup D_{2} = 1 | D_{1} \neq D_{2}] = \frac{P [(D_{1} = 1 \cup D_{2} = 1) \cap (D_{1} \neq D_{2})]}{P [D_{1} \neq D_{2}]}

(2) Count favorable and total outcomes:

There are $2 \cdot 6 - 1 = 11$ combinations with at least one $1$ . Excluding $(1,1)$ gives $10$ combinations where the outcomes also differ.

There are $36 - 6 = 30$ combinations where the two dice differ.

(3) Evaluate:

\begin{matrix} P [D_{1} = 1 \cup D_{2} = 1 | D_{1} \neq D_{2}] = \frac{10 / 36}{30 / 36} \\ ≫ ≫ \frac{1}{3} \end{matrix}

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