Question

Unknown to a medical researcher, 8 out of 24 patients have a heart problem that will result in death if they receive the test drug. 10 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 = 10, p = 0.3333, (1 - p) = 0.6667 and x = 1
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) = (10C2 * 0.3333^2 * 0.6667^8) + (10C3 * 0.3333^3 * 0.6667^7) + (10C4 * 0.3333^4 * 0.6667^6) + (10C5 * 0.3333^5 * 0.6667^5) + (10C6 * 0.3333^6 * 0.6667^4) + (10C7 * 0.3333^7 * 0.6667^3) + (10C8 * 0.3333^8 * 0.6667^2) + (10C9 * 0.3333^9 * 0.6667^1) + (10C10 * 0.3333^10 * 0.6667^0)
P(X > 1) = 0.1951 + 0.2601 + 0.2276 + 0.1365 + 0.0569 + 0.0162 + 0.003 + 0.0003 + 0
P(X > 1) = 0.8959