Problem 1017

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.

 

Solution:-

 

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

=70(0.71639296)(0.00004096)

=0.0021

 

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