Question

Assume that random guesses are made for six six multiple choice questions on an SAT​ test, so that there are n equals = 6 6 ​trials, each with probability of success​ (correct) given by p equals = 0.35 0.35. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4 4.

Answer 1

This is a direct application of Binomial distribution with sample size (n) = 6 and P(success) = p = 0.35

Let X be a Binomial random variable.

X ~ Binomial (n = 6, p = 0.35)

We want to find, P(X < 4)

Using Excel we find this probability,

P(X < 4) = P(X ≤ 3) = BINOMDIST (3, 6, 0.35, 1) = 0.8826

=> P(X < 4) = 0.8826

Therefore, required probability is 0.8826