.
Dave has just left an interview with a prospective employer.
The hiring manager told Dave that she will tolerate one mistake during his first year
but will fire him if he makes two mistakes.
Based on Dave’s research and understanding of the job, he estimates that he will have
to make five critical decisions during the year, and with his knowledge of the processes,
figures that he will have about an 80% chance of making any of those five decisions correctly.
Dave does not want to run any more than a 25% chance of being fired.
If each of the decisions is independent of the others, should Dave risk taking the job
if offered? Explain why or why not.
~~~~~~~~~~~~~~~
It is the Binomial probability distribution problem.
In this problem, the number of trials is 5 (five critical decisions);
the probability to make an error in each of the individual decisions is 0.2;
the number of successful trials is 2 (there is playing words here: the "successful" is a mistaken decision).
We should estimate the probability making at least two mistakes.
The probability to make at least two mistakes is
P = .
To facilitate my 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 = P(n=5, k=>2, p= 0.2) = 0.26272 = 0.2627 = 26.27% (rounded). ANSWER
This probability is higher than 25%.
So, based on this analysis, Dave should not take the risk.
Solved.
----------------
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).