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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
Solved.