Lymnozyme cures most infections in Koi fish caused by bacteria; in fact, it has been shown to be 98% effective if used according to the directions. If 11 Koi with a bacterial infection are treated, what is the probability that 10 of the fish are cured?
A) 0.1788
B) 0.1798
C) 0.1973
D) 0.9481
E) 0.1767

Question

Lymnozyme cures most infections in Koi fish caused by bacteria; in fact, it has been shown to be 98% effective if used according to the directions. If 11 Koi with a bacterial infection are treated, what is the probability that 10 of the fish are cured? ​
A) 0.1788
B) 0.1798
C) 0.1973
D) 0.9481
E) 0.1767

Quizplus · Accepted Answer

This is a binomial probability problem, where success is defined as a Koi being cured and failure as a Koi not being cured. The probability of success (cure) is 0.98 and the probability of failure (not cured) is 0.02 (1 - 0.98). We want to find the probability that exactly 10 Koi out of 11 are cured, which can be represented as:

P(X = 10) = (11 choose 10) * 0.98^10 * 0.02^1

Using a calculator, we get:

P(X = 10) = 0.1798

Therefore, the best choice is B.

Lymnozyme Cures Most Infections in Koi Fish Caused by Bacteria;