Question

In a hospital 60% of the patients are married. What’s the probability that a sample of one word with 8 patient, had 3 were married

Answer 1

Question #71922, Math / Statistics and Probability

In a hospital 60% of the patients are married. What's the probability that a sample of one word with 8 patient, had 3 were married

Solution

Assuming the sample size of 8 is less than 5% of the total number of patients in the hospital.

Using binomial probability formula.

$$p(x) = \frac{n!}{(n - x)!x!} p^x q^{n - x};$$ $$p(3) = \frac{8!}{(8 - 3)!3!} 0.6^3 0.4^{8 - 3} = 0.1239$$

Answer: the probability that in a random sample of 8 patients 3 are married is 0.1239.

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