In a simultaneous throw of a pair of dice, what is the probability of getting a total more than 8?

When throwing two dice simultaneously, the goal is to find the probability that the sum of both dice is more than 8.

More than 8 means: 9, 10, 11, or 12

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When throwing 2 dice:

• First die can show: 1, 2, 3, 4, 5, or 6 (6 options)
• Second die can show: 1, 2, 3, 4, 5, or 6 (6 options)

Total possible outcomes $= 6 \times 6 = 36$

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All combinations where the sum is more than 8:

Sum $= 9$: (3,6), (4,5), (5,4), (6,3) → 4 ways

Sum $= 10$: (4,6), (5,5), (6,4) → 3 ways

Sum $= 11$: (5,6), (6,5) → 2 ways

Sum $= 12$: (6,6) → 1 way

Total favorable outcomes $= 4 + 3 + 2 + 1 = 10$

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Probability $= \frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

Probability $= \frac{10}{36}$

Probability $= \frac{5}{18}$

Therefore, the probability of getting a total more than 8 is $\frac{5}{18}$.