.
It is a standard binomial distribution problem.
Part ( a )
The number of trials is n=25; the number of successful trials is 15;
the probability of success for each single individual trial is p = 0.75.
The formula to calculate the probability is
P = P(n=25; k=15; p=0.75) = = .
The resulting number is P = 0.041658351 = 0.04166 (rounded). ANSWER
Part (a) is solved.
Solve part (b) in the same way.
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If you want to see many similar (or different) solved problems, look into the lessons
- Simple and simplest probability problems on Binomial distribution
- Typical binomial distribution probability problems
- How to calculate Binomial probabilities with Technology (using MS Excel)
- Solving problems on Binomial distribution with Technology (using MS Excel)
- Solving problems on Binomial distribution with Technology (using online solver)
in this site.
After reading these lessons, you will be able to solve such problems on your own,
which is your PRIMARY MAJOR GOAL visiting this forum (I believe).