Answer to Question #244658 in Statistics and Probability for sink

Question

Assume that random guesses are made for nine multiple choice questions on an SAT​ test, so that there are n=9 ​trials, each with probability of success​ (correct) given by p=0.2. Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than 4.

Answer 1

This is a binomial distribution with p=0.2, n=9.

$P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=$

$=C_9^00.2^00.8^9+C_9^10.2^10.8^8+C_9^20.2^20.8^7+C^3_90.2^30.8^6=$

$=0.1342+0.3020+0.3020+0.1762=0.9144.$