Final answer:
There is approximately an 80.31% chance that at least one of the 10 horses admitted to the clinic has been infected with West Nile virus. This is found by calculating the probability that none has the virus (85%^10) and subtracting it from 1.
Step-by-step explanation:
To calculate the probability that at least one of the horses admitted to the clinic has West Nile virus, we first need to find the probability that none of the horses has the virus. The probability that a horse does not have the virus is 85%, since 15% of the horses typically have the virus.
We then raise this probability to the power of the number of horses, which in this case is 10:
(0.85)10 ≈ 0.1969
This result is the probability that none of the 10 horses has West Nile virus. To find the probability that at least one horse has the virus, we subtract this probability from 1:
1 - (0.85)10 ≈ 1 - 0.1969 ≈ 0.8031
So, there is approximately an 80.31% chance that at least one of the 10 horses admitted to the clinic has been infected with West Nile virus.