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Six questions are in a multiple choice quiz. Each question has 5 possible answers.
A student guesses at each question.
a) Find the probability that the student passes (earns at least 50%)
b) What is the student's expected number of correct answers?
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Answering randomly, the probability to answer each separate multiple choice question correctly is ;
answering incorrectly is .
The answers to 6 questions of the quiz are independent events.
So, we have a binomial distribution with 6 trials; the probability of success is = 0.2 in each
individual trial and the problem asks in part (a) about probability of 3 or more success trials.
The formula is
P = P(3) + P(4) + P(5) + P(6) = = .
It can be calculated manually, or using technology.
To facilitate calculations, I used online calculator at this site https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
The resulting number is P = 0.09888 (rounded).
It is the ANSWER to question (a).
For question (b), math expectation of binomial distribution is E = n*p = 6*0.2 = 1.2.
Solved.
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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).