Question

The success rate of corneal transplant surgery is 94%. The surgery is performed on 5 patients. Find the probabitity that

(a) exactly four surgeries are suscessful.

Answer 1

The probability of exactly four surgeries being successful in a corneal transplant surgery is 23.09%.

Step-by-step explanation:

To find the probability that exactly four surgeries are successful, we need to use the binomial probability formula. The formula is:

P(x) = C(n, x) * p^x * (1-p)^(n-x)

Where:

• P(x) is the probability of getting x successes
• C(n, x) is the number of combinations of selecting x successes out of n trials
• p is the probability of success
• (1-p) is the probability of failure
• n is the number of trials
• x is the number of successful surgeries

In this case, n = 5 (number of surgeries), p = 0.94 (success rate), and x = 4 (number of successful surgeries).

Plugging in these values, we get:

P(4) = C(5, 4) * 0.94^4 * (1-0.94)^(5-4)

Simplifying further:

P(4) = 5 * 0.94^4 * 0.06^1

P(4) = 5 * 0.7699 * 0.06

P(4) = 0.2309

Therefore, the probability that exactly four surgeries are successful is 0.2309, or 23.09%.