Question

A surgery has a success rate of 75%. Suppose that the surgery is performed on 4 patients. What is the probability that the surgery is successful on exactly 3 patients?

Answer 1

0.21094 is the probability that the surgery is successful on exactly 3 patients.

What is probability?

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

According to the given question,

Let Y = The number of patients who respond yes: $Y - Bin (n,p)$

Given , $n = 4 , p = 0.75 , q = 1 - p = 0.25$

$P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094$

The probability that the surgery is successful on exactly 3 patients is 0.21094

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