Answer to Question #227913 in Statistics and Probability for Teddy

Question

Hospital records show that of patients suffering from a certain disease, 25% die
of it.
(i) What is the probability that of 6 randomly selected patients, 4 will recover?

Answer 1

Let X be the binomial random variable denoting the number of patients.

 Let p be the probability that the patient will recover and q be the probability that patient will die.

According to the problem, q = 75% = 0.75 and p = 25% = 0.25 and n = 6

P(X=4) = C⁴₆ * p⁴ * q² = 15 * 0.25⁴ * 0.75² = 0.03296