Question

A certain production experiment is to be repeated 12 times, and each trial has a 40% chance of success. What are the chances that at least a quarter of the trials are successful?

(A) 8.3%                       (B) 14.2%                         (C) 22.5%                            (D) 77.5%                                (E) 91.7%

Answer 1

p = 0.4 and n = 12
quarter of 12 times = 3

P(X >= 3)
= 1 - P(X <= 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - (0.6^12 + 12C1 * 0.4^1 * 0.6^11 + 12C2 * 0.4^2 * 0.6^10)

= 0.9166

i.e. 91.7%

option E