Question

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.
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.

Explanation:

Step1: Count total outcomes

The table is a 6x6 grid (since two dice, each with 6 faces), so total outcomes = \(6\times6 = 36\).

Step2: Identify favorable outcomes (even sum <9)

List even sums less than 9: 2,4,6,8.

• Sum=2: 1 outcome (1,1)
• Sum=4: 3 outcomes (1,3),(2,2),(3,1)
• Sum=6: 5 outcomes (1,5),(2,4),(3,3),(4,2),(5,1)
• Sum=8: 5 outcomes (2,6),(3,5),(4,4),(5,3),(6,2)

Total favorable = \(1 + 3 + 5 + 5 = 14\).

Step3: Calculate probability

Probability = \(\frac{\text{favorable}}{\text{total}}=\frac{14}{36}\approx0.39\) (rounded to nearest hundredth).

Answer:

\(0.39\)