Lymnozyme cures most infections in Koi fish caused by bacteria; in fact, it has been shown to be 91% effective if used according to the directions. If 5 Koi with a bacterial infection are treated, what is the probability that 4 of the fish are cured?
A) 0.3086
B) 0.3261
C) 0.8837
D) 0.3076
E) 0.3055

Question

Lymnozyme cures most infections in Koi fish caused by bacteria; in fact, it has been shown to be 91% effective if used according to the directions. If 5 Koi with a bacterial infection are treated, what is the probability that 4 of the fish are cured? ​
A) 0.3086
B) 0.3261
C) 0.8837
D) 0.3076
E) 0.3055

Quizplus · Accepted Answer

This is a binomial probability problem where the probability of success (curing a fish) is 0.91, and we want exactly 4 successes out of 5 trials. The formula for binomial probability is P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time, p is the probability of success, and n is the number of trials. Plugging in the values, we get P(4 out of 5) = C(5, 4) * 0.91^4 * (1-0.91)^1 = 5 * 0.6859 * 0.09 ≈ 0.3086.

Lymnozyme Cures Most Infections in Koi Fish Caused by Bacteria;