Solutions - 5030-02

(1) Set up the conditional probability formula:

P [D_{1} + D_{2} = 10 | D_{1} = 5 \cup D_{2} = 5] = \frac{P [(D_{1} + D_{2} = 10) \cap (D_{1} = 5 \cup D_{2} = 5)]}{P [D_{1} = 5 \cup D_{2} = 5]}

(2) Count favorable and total outcomes:

There is $1$ combination where at least one die is a $5$ and the sum is $10$ : $(5,5)$ .

There are $2 \cdot 6 - 1 = 11$ combinations where at least one die is a $5$ .

(3) Evaluate:

\begin{matrix} P [D_{1} + D_{2} = 10 | D_{1} = 5 \cup D_{2} = 5] = \frac{1 / 36}{11 / 36} \\ ≫ ≫ \frac{1}{11} \end{matrix}

ProbabilityHome