A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability that 2 or fewer horses among the 10 horses admitted have been infected with West Nile virus?

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula, which 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 a single trial, and (n choose k) is the binomial coefficient. In this case, n = 10 (horses), p = 0.15 (probability of a horse having West Nile virus), and we're interested in the probability of k = 0, 1, or 2 horses having the virus. We calculate the probabilities for each of these cases and sum them up to find the total probability of 2 or fewer horses being infected. The correct answer, 0.8202, reflects the cumulative probability of these scenarios, indicating that there's an 82.02% chance that 2 or fewer out of the 10 horses admitted will have West Nile virus.

A Local Veterinary Clinic Typically Sees 15% of Its Horses