Question

Microffacture knee surgery has a 68% chance of success on patients with degenecative knees. The surgery is performed on four pasents Find the probabbity of the surger being successful an exsctly two patients. (Round your answer to Three decimal plsces)

Answer 1

The probability that microfracture knee surgery is successful in exactly two out of four patients with a 68% success rate per patient is approximately 28.4%, or 0.284 when rounded to three decimal places.

Step-by-step explanation:

The question is asking for the probability of microfracture knee surgery being successful in exactly two out of four patients, given that each surgery has a 68% chance of success. This problem can be solved using the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

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Plugging the values into the formula, we have:

P(X=2) = (4 choose 2) * (0.68)^2 * (0.32)^2

Calculating the binomial coefficient (4 choose 2) and the remaining terms, rounding to three decimal places:

P(X=2) ≈ 6 * 0.4624 * 0.1024 ≈ 0.284

Thus, the probability that exactly two out of four patients will have a successful knee surgery is 0.284, or 28.4%, when rounded to three decimal places.