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 $P ( 5 )$
A) 0.2095
B) 0.0001
C) 0.1571
D) 0.0873

Question

Quizplus · Accepted Answer

$X$ follows a binomial distribution with $n = 13$ and $p = 0.5$ (since each guess has a 50% chance of being correct). The probability of getting exactly 5 correct answers is calculated using the binomial probability formula: $$P(X = k) = \binom{n}{k}p^k(1-p)^{n-k}$$ Substituting $n = 13$, $k = 5$, and $p = 0.5$ gives: $$P(5) = \binom{13}{5}(0.5)^5(0.5)^{13-5} = 0.1571$$

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

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