A student takes a true-false test that has 13 questions and guesses randomly at each answer. Let $X$ be the number of questions answered correctly. Find $P ( 11$ or more)
A) 0.0112
B) 0.0017
C) 0.0461
D) 0.9539

Question

Quizplus · Accepted Answer

The probability of guessing any question correctly is 0.5 since it's a true/false question. To find the probability of getting 11, 12, or 13 questions right, we use the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=13$, $p=0.5$, and $k$ is the number of correct answers (11, 12, or 13 in this case). Calculating for each and summing up gives the total probability of getting at least 11 questions right, which is approximately 0.0112.

A Student Takes a True-False Test That Has 13 Questions XXX

A Student Takes a True-False Test That Has 13 Questions $X$