Question

A pair of dice is cast and the numbers that show on the dice are observed. Find the probability that one die shows 6 and the other is a number less than 3.

Answer 1

Since each die has 6 faces, the probability of getting 6 points on the first die is

${p_1} = \frac{1}{6}$

The probability of getting a number less than 6 is

${p_2} = \frac{2}{6} = \frac{1}{3}$ (1 or two points).

Then the wanted probability is

$p = {p_1}{p_2} = \frac{1}{6} \cdot \frac{1}{3} = \frac{1}{{18}}$

Answer: $p = \frac{1}{{18}}$