When treated with an antibiotic 97 percent of all the dolphins are cured of an ear infection If 7 dolphins are treated find the probability that exactly 4 are cured?

To find the probability that exactly 4 out of 7 dolphins are cured when treated with an antibiotic, we can use the binomial probability formula:

[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} ]

where ( n = 7 ), ( k = 4 ), and ( p = 0.97 ). Calculating this gives:

[ P(X = 4) = \binom{7}{4} (0.97)^4 (0.03)^3 ]

Calculating the combination and the probabilities, we find that the probability of exactly 4 dolphins being cured is approximately 0.0008 or 0.08%.