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In: Statistics and Probability

The success rate of corneal transplant surgery is 85%. The surgery is performed on six patients....

The success rate of corneal transplant surgery is 85%. The surgery is performed on six patients.
What is the probability of the surgery being successful on four patients?

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Expert Solution

Solution :

Let X be a random variable which represents out of 6 corneal transplant surgeries, the number of successful surgeries.

The success rate of corneal transplant surgery is 85%.

Probability of success (p) = 0.85

Number of trials (n) = 6

Since, probability of success remains constant in each of the trials, we have only two mutually exclusive outcomes for each of the trials, number of trials are finite and outcomes are independent, therefore we can consider that X follows binomial distribution with parameters n = 6 and p = 0.85.

We have to find P(X = 4)

According to binomial probability law, probability of occurrence of exactly x successes in n trials is given by,

Where, p is probability of success.

The probability of the surgery being successful on four patients is 0.1762.

Please rate the answer. Thank you.

orchestra answered 1 year ago
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