Question

For a three-question multiple-choice pop quiz, a student is totally unprepared and randomly guesses the answer to each question. If each question has four options, then the probability of selecting the correct answer for any given question is 1/4, or .25. With guessing, the response on one question is not influenced by the response on another question. Thus, whether one question is answered correctly is independent of whether or not another question is answered correctly. Find the probability the student passes, answering at least two questions correctly.

Answer 1

This can be solved using the binomial distribution.
\[\large P(2)=3\times0.25^{2}\times0.75\ ........(1)\]
\[\large P(3)=0.25^{3}\ ...................(2)\]
The probabilities of getting 2 or 3 answers correct are found from equations (1) and (2).
To find the probability the student passes, answering at least two questions correctly add the results of (1) and (2):
\[\large P(2\ or\ 3\ correct)=P(2)+P(3)=you\ can\ calculate\]