Question

Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 12?

Answer 1

We know we're dealing with two dice. Since each die has 6 different possibilities, the outcomes of rolling two dice are given by:

6 × 6, which is 36. This will be our denominator.

How many ways can we get 9 or 12 with two dices?

For a sum of 9:

3 + 6 = 9

4 + 5 = 9

There are two possibilities.

For a sum of 12:

6 + 6 = 12

There is only one possibility.

Summing it up, there are 3 possibilities to get a sum of 9 or 12 with the two dice.

The events are independent events since neither of them can ever occur at the same time.

Thus, the probability will be:

`\text{ Probability = \lparen Probability of getting 9\rparen + \lparen Probability of getting 12\rparen}`

We get,

`\text{ Probability = }(2)/(36)\text{ + }(1)/(36)\text{ = }(3)/(36)\text{ = }(1)/(12)\text{ \lparen simplified\rparen}`

Therefore, the probability is 1/12.