Final answer:
The probability of getting at least two eights when rolling a ten-sided die 16 times is calculated using the complementary probability of getting zero or one eight. The calculation using the binomial probability formula yields a probability of 3.68%, corresponding to answer D.
Step-by-step explanation:
The probability of rolling an 8 on a ten-sided die is 1 out of 10, or 0.1. To find the probability of getting the value of 8 at least twice when rolling the die 16 times, we need to consider all the scenarios where we get two or more eights. This scenario is the complement of the scenario where we get zero or one eight. We can use the binomial probability formula, which in general form is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the number of trials, 'k' is the number of successes, 'p' is the probability of success on an individual trial, and '(n choose k)' is the binomial coefficient.
We need to calculate the probabilities for getting exactly zero eights and exactly one eight and subtract these from 1 to find the probability of getting at least two eights. The calculations are as follows:
- P(X = 0) = (16 choose 0) * (0.1)^0 * (0.9)^16
- P(X = 1) = (16 choose 1) * (0.1)^1 * (0.9)^15
We then subtract the sum of these two probabilities from 1 to get the probability of getting at least two eights:
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
After calculating and summing these probabilities, we find that the probability, expressed as a percentage to two decimal places, is 3.68%, which corresponds to answer D.