Question

Unknown to a medical researcher, 6 out of 18 patients have a heart problem that will result in death if they receive the test drug. 8 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that more than 1 patient will die? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Here, n = 8, p = 0.3333, (1 - p) = 0.6667 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > 1).
P(X > 1) = (8C2 * 0.3333^2 * 0.6667^6) + (8C3 * 0.3333^3 * 0.6667^5) + (8C4 * 0.3333^4 * 0.6667^4) + (8C5 * 0.3333^5 * 0.6667^3) + (8C6 * 0.3333^6 * 0.6667^2) + (8C7 * 0.3333^7 * 0.6667^1) + (8C8 * 0.3333^8 * 0.6667^0)
P(X > 1) = 0.2732 + 0.2731 + 0.1707 + 0.0683 + 0.0171 + 0.0024 + 0.0002
P(X > 1) = 0.8049