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A quiz consists of 10 multiple-choice questions, each with 5 possible answers.
For someone who makes random guesses for all of the answers, find the probability
of passing if the minimum passing grade is 40 %.
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To pass, 40% (or MORE) of 10 questions should be answered/guessed correctly.
40% of 10 means that 4 questions or more should be answered/guessed correctly.
In other words, at least 4 questions should be answered/guessed correctly.
The probability to guess correctly for each individual question is 1/5 = 0.2.
Guessing provides independent results for each of 10 questions.
So, we have the binomial distribution problem with 10 trials;
the probability of success is 0.2 for each trial.
We want to find the probability of having 4 or more successes.
It can be done by several different ways.
(1) First, you may use spreadsheet like MS excel and calculate the probability of success
of binomial distribution for values of trials k = 4, 5, 6, 7, 8, 9 10, and add them.
(2) More short way is to use the standard Excel function BINOM.DIST in the mode, which gives
the cumulative distributions values as the output.
About this function read from this web-site
https://corporatefinanceinstitute.com/resources/excel/binomial-distribution-excel/
Then the formula to get the answer in this problem is P = 1 - BINOM.DIST(3, 10, 0.2, TRUE)
(3) Alternatively, you may use a regular calculator TI-83/84 and its standard function
binomcdf, which produces cumulative function output, too.
About this function read from this web-site
https://www.mathbootcamps.com/binomial-probabilities-ti-83-or-84-calculator/
Then the formula to get the answer in this problem is P = 1 - binomcdf(10, 0.2, 3).
(4) Finally, you can use an online calculator (free of charge) at this web-site
https://stattrek.com/online-calculator/binomial.aspx
This calculator has simple and convenient interface, so any student, even
a beginner, can easily work with it.
The ANSWER to the problem's question is P = 0.12087 (rounded).
Solved.