Question

the sample space for a roll of two number cubes is shown in the table.
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 two numbers rolled can be added to get a sum Find P sum is less than 4.

Answer 1

The sums less than 4 are 2 and 3. From the table, we can see that there is only one way to get a sum of 2 (rolling a 1 on both cubes) and two ways to get a sum of 3 (rolling a 1 and a 2). Therefore, there are a total of 3 outcomes that result in a sum less than 4.

Since there are 36 equally likely outcomes in the sample space, the probability of getting a sum less than 4 is:

P(sum < 4) = number of outcomes that result in a sum less than 4 / total number of outcomes

P(sum < 4) = 3/36 = 1/12

Therefore, the probability of getting a sum less than 4 is 1/12.