A student takes a true-false test that has 15 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(Fewer than 4)
A)0.9408
B)0.0176
C)0.0592
D)0.0037

Question

Quizplus · Accepted Answer

The probability of answering a question correctly by guessing is 1/2. The probability of answering fewer than 4 questions correctly is the sum of the probabilities of answering 0, 1, 2, or 3 questions correctly. These probabilities can be calculated using the binomial distribution:P(X = 0) = (1/2)^15 = 0.0037P(X = 1) = 15 * (1/2)^15 = 0.0592P(X = 2) = 105 * (1/2)^15 = 0.1776P(X = 3) = 455 * (1/2)^15 = 0.3552Therefore, P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0037 + 0.0592 + 0.1776 + 0.3552 = 0.6007.

A Student Takes a True-False Test That Has 15 Questions