When treated with an antibiotic, 92% of all dolphins are cured an ear infection. If 8 dolphins are treated, find the probability that exactly 4 are cured.
Assuming the events are independent, then the probability of obtaining exactly x successes, P(x), in n independent trials is given by P(x) = (nCx) pxqn-x where p is the probability of success on a single trial and q is the probability of failure on a single trial.
We will consider a ‘success’ a dolphin being cured.
The probability a dolphin is cured is 0.92.
The probability a dolphin is not cured is thus 1 – 0.92, or 0.08.
Thus, n = 8, x = 4, p = 0.92, and q = 0.08.
Substitute the values.
P(4) = (8C4)(0.92)4(0.08)4