Question

Two six-sided dice are rolled. Using the sample space for rolling two dice shown in the figure below, find the probability that the sum of the dice is either 4 or 7. Give your answer as a reduced fraction.

Answer 1

Explanation:

There are 36 ways 2 dice can be thrown. Sometimes colors are used to tell the difference between the dice.

36 comes from 6*6

Suppose you have 2 dice 1 blue and the other white

Blue White

1 1

2

3

4

5

6

There's 6 ways that have been thrown. Then you go to the blue dice being 2. You get six more. Then 3 gives you six more 4 gives you another six. and so on. The whole procedure adds to 36

you can throw a four 3 ways

Blue white

1 3

3 1

2 2

You can throw 7 six ways

Blue white

1 6

6 1

2 5

5 2

3 4

4 3

So of the 36 ways to throw the dice 9 will successful. (6 + 3)

Answer: 9/36 = 1/4 times you will be successful