Question

The sample space for a roll of two number cubes is shown in the table.
what is the probability that the roll will result in both numbers being the same?

Answer 1

To find the probability of rolling the same number on two number cubes, we need to count the number of ways we can do this. There are six ways to roll any given number on each cube, so there are six ways to roll doubles (1-1, 2-2, 3-3, 4-4, 5-5, and 6-6) out of a total of 36 possible outcomes. Thus, the probability of rolling doubles is 6/36 or 1/6, which reduces to approximately 0.1667 or 16.67%.

Answer 2

The sample space for rolling two number cubes consists of all possible ordered pairs of numbers that can be obtained by rolling two dice. There are 6 possible outcomes for each die roll, so the sample space consists of 6x6=36 possible outcomes.

To find the probability that the roll will result in both numbers being the same, we need to count the number of outcomes where both numbers are the same, and divide by the total number of possible outcomes.

There are 6 ways to roll doubles: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). Therefore, the probability of rolling doubles is:

P(doubles) = number of outcomes where both numbers are the same / total number of possible outcomes
P(doubles) = 6/36 = 1/6

So the probability that the roll will result in both numbers being the same is 1/6 or approximately 0.1667, which is the same as 16.67%.