Final answer:
To find the probability of rolling an 8 at least twice in 16 rolls of a 10-sided die, we can use the binomial distribution formula to calculate the probabilities for each possible number of times rolling an 8. Summing up these probabilities gives us the total probability.
Step-by-step explanation:
To find the probability that a single ten-sided die comes up showing the value of 8 at least twice in 16 rolls, we need to calculate the probability of getting 8 exactly twice, 8 exactly three times, and so on, up to all 16 rolls being 8. We can then sum up these probabilities to get the total probability.
The probability of getting 8 exactly k times in 16 rolls can be calculated using the binomial distribution formula:
P(k) = (16 Choose k) * (1/10)^k * (9/10)^(16-k)
Summing up the probabilities for k = 2, 3, ..., 16 will give us the final probability. Calculating this probability gives us approximately 13.17%.