A multiple choice test consists of eight questions each of w

A multiple choice test consists of eight questions, each of which has four choices. Each question has exactly one correct answer. William guesses randomly at each answer. What is the probability that he gets six or fewer questions correct?

Solution

binomial distribution

P ( x <= 6 ) = 1 - P( x > 6 ) = 1 - P(x=7 +P(x=8)

n = 8

p = 1/4

q = 3/4

P(x=7) = 8C 7 * 1/4 ^7   * 3/4 ^8-7 = 0.000366

P(x=8) = 8C8 * 1/4 ^8   * 3/4 ^8-8 =0.000015

P ( x <= 6 ) = 1 - 0.00038 = 0.9996