Question

A pair of dice is rolled. what is the probability that you roll an even number or a 3?

Answer 1

A pair of dice is rolled.

Each dice has 6 outcomes.

So, the total number of outcomes for a pair of dice is 6×6 = 36

These 36 outcomes are given below

(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)

The probability that you roll an even number is given by

There are 9 such outcomes where you can have an even number

(2, 2) (2, 2) (2, 6) (4, 2) (4, 4) (4, 6) (6, 2) (6, 4) (6, 6)

`P(even)=(9)/(36)`

The probability that you roll a 3 is given by

There are 11 such outcomes where you can roll a 3

(1, 3) (2, 3) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 3) (5, 3) (6, 3)

`P(3)=(11)/(36)`

Finally, the probability that you roll an even number or a 3 is

`\begin{gathered} P(even\: or\: 3)=P(even)+P(3) \\ P(even\: or\: 3)=(9)/(36)+(11)/(36) \\ P(even\: or\: 3)=(5)/(9) \end{gathered}`

Therefore, the probability is 5/9