Answer to Question #113884 in Statistics and Probability for Richard Bassey

Question

A die was thrown twice. Find the probability of getting a 3 or 6.

Answer 1

When a die is thrown twice, there are 36 possible outcomes.

$$\begin{matrix} (1,1) & (1,2) & (1,3) & (1,4) & (1,5) & (1,6)\\ (2,1) & (2,2) & (2,3) & (2,4) & (2,5) & (2,6) \\ (3,1) & (3,2) & (3,3) & (3,4) & (3,5) & (3,6) \\ (4,1) & (4,2) & (4,3) & (4,4) & (4,5) & (4,6)\\ (5,1) & (5,2) & (5,3) & (5,4) & (5,5) & (5,6) \\ (6,1) & (6,2) & (6,3) & (6,4) & (6,5) & (6,6) \end{matrix}$$

There are 20 favorable outcomes

$$\begin{matrix} (1,3) & (1,6) & (2,3) & (2,6) & (3,1) & (3,2)\\ (3,3) & (3,4) & (3,5) & (3,6) & (4,3) & (4,6) \\ (5,3) & (5,6) & (6,1) & (6,2) & (6,3) & (6,4) \\ (6,5) & (6,6) \end{matrix}$$

Find the probability of getting a 3 or 6

$$P(3\ or\ 6)={20 \over 36}={5 \over 9}$$