Question

An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any​ other, find the probability that the sum of the dots is 4 or 9.

Answer 1

When dices are rolled, the dots facing up represent the outcome of the dice.

So,when two fair dices are rolled,there are 6 likely outcomes in dice 1 and 6 likely outcomes in dice 2. This makes it a total of 36 outcomes .

Therefore, sample space in this case is 36

Now, out of these 36 outcomes, events when the sum is 4 are (1,3),(2,2),(3,1) , which in total are 3

Events when the sum is 9 are (3,6),(4,5),(5,4),(6,3) which in total are 4.

Therefore, total events when the sum is either 4 or 9 = 3 + 4 = 7 (as they are mutually exhaustive , there are no overlaps of the events)

Therefore, probability that the sum is either 4 or 9 = Total events/ Total sample space = 7/36