Question

Suppose you have 8 dice. When all of them roll, what are the chances that there is at least one 6?

A) 34.77%

B) 43.14%

C) 38.79%

D) 46.28%

Answer 1

To find the probability of rolling at least one 6 with 8 dice, calculate the complementary probability (no 6s) and subtract it from 1. The proper calculation shows a probability of 76.72%, which is not among the given options, suggesting an error in the question or choices.

Step-by-step explanation:

The question is about calculating the probability that at least one of 8 dice will show a 6 when rolled. To solve this, it's easier to calculate the probability of the complementary event, which is that none of the dice will show a 6, and then subtract this from 1.

Each die has a ⅕ (or 5/6) chance of not showing a 6. Since each die is independent, we multiply the probability for one die by itself 8 times:

(5/6) × (5/6) × (5/6) × (5/6) × (5/6) × (5/6) × (5/6) × (5/6) = (5/6)^8.

Calculating this gives approximately 0.2328 or 23.28%. This is the probability that no 6 will appear. Therefore, the probability that at least one 6 will appear is:

1 - 0.2328 = 0.7672 or 76.72%.

The correct answer is not listed in the choices given, indicating a possible mistake in the question or the choices provided. The closest choice to the correct answer would be ‘D) 46.28%’, but this is still significantly lower than the correct value.