SOLUTION: A civil service multiple-choice exam consists of 100 questions with 4 choices per question. Suppose a candidate randomly guesses the answer to every question. Find the probability

It is a binomial distribution probability problem.


     - number of trials        n =  100;
     - number of success trial k <   40;
     - Probability of success on a single trial p =  = 0.25.



We need calculate  P(n=100; k < 40; p=0.25).      


To facilitate calculations, I use an online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


It provides nice instructions  and  a convenient input and output for all relevant options/cases.


    P(n=100; k < 40; p=0.0.25) = 0.99931340779,   or   0.9993 (rounded).       ANSWER