Question

A group is playing a game that uses two number cubes labeled 1 to 6. A player rolls the number cubes and finds the sum of the numbers rolled. The set of all possible outcomes is shown in the table.



Possible Sums
2

3

4

5

6

7

3

4

5

6

7

8

4

5

6

7

8

9

5

6

7

8

9

10

6

7

8

9

10

11

7

8

9

10

11

12




If the sum is even and less than 9, the player moves the number spaces equal to the sum. Otherwise, the player does not move.

Question
What is the probability that a player will move on a turn? Round the answer to the nearest hundredth. Enter the answer in the box.

Answer 1

To solve the problem, we first need to determine which sums are even and less than 9. The possible sums when rolling two six-sided dice (number cubes) range from 2 to 12 (as evidenced by the table).

The even sums less than 9 are:
- 2
- 4
- 6
- 8

Next, we will check how many possible outcomes yield these sums:

1. **Sum of 2:** (1,1) → 1 outcome
2. **Sum of 4:** (1,3), (2,2), (3,1) → 3 outcomes
3. **Sum of 6:** (1,5), (2,4), (3,3), (4,2), (5,1) → 5 outcomes

So we can summarize:
- The sum of 2 has 1 outcome.
- The sum of 4 has 3 outcomes.
- The sum of 6 has 5 outcomes.

Now we add these outcomes together:
- Total outcomes resulting in moving: 1 + 3 + 5 = 9 outcomes.

Next, we calculate the total number of possible outcomes when rolling two dice. Since each die has 6 faces, the total number of outcomes is:
\[
6 \times 6 = 36.
\]

Now we can find the probability that a player will move:
\[
\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{9}{36} = \frac{1}{4} = 0.25.
\]

Rounding to the nearest hundredth, the probability that a player will move on a turn is:
\[
\boxed{0.25}.
\]