Solutions - 5070-04

There are $36$ total outcomes when rolling two dice.

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(1) Compute $P[A]$:

Desired outcomes for sum $=10$: $(4,6)$, $(5,5)$, $(6,4)$ — 3 outcomes.

$$P[A]=\frac{3}{36}=\frac{1}{12}$$

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(2) Compute $P[B]$:

Desired outcomes for sum $=12$: $(6,6)$ — 1 outcome.

$$P[B]=\frac{1}{36}$$

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(3) Compute $P[C]$:

Desired outcomes for equal numbers: $(\mathrm{1,1})$, $(\mathrm{2,2})$, $(\mathrm{3,3})$, $(\mathrm{4,4})$, $(\mathrm{5,5})$, $(\mathrm{6,6})$ — 6 outcomes.

$$P[C]=\frac{6}{36}=\frac{1}{6}$$