Question

A student takes a 20 question true/false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 15 correct out of 20. Would you consider this event likely to occur?

Answer 1

yes

Answer 2

This can be solved using the binomial distribution to find the probability of guessing correctly the answers to 15 or more questions:
\[P(15\ correct)=\left(\begin{matrix}20 \\ 15\end{matrix}\right)0.5^{15}0.5^{5}=\frac{20!}{15!5!}0.5^{20}=0.01478\]
\[P(16\ correct)=\left(\begin{matrix}20 \\ 16\end{matrix}\right)0.5^{16}0.5^{4}=you\ can\ calculate\]
Then you need to calculate in a similar way the probabilities of guessing 17, 18, 19 and 20 answers correctly. Finally the six values of probability are added to find the required probability.