SOLUTION: A multiple-choice test consists of 25 questions, each of which has five possible answers. A score of 14 or more is considered passing. If you know the correct answers to five quest
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Question 509235: A multiple-choice test consists of 25 questions, each of which has five possible answers. A score of 14 or more is considered passing. If you know the correct answers to five questions and guess on the rest, find the probability that you pass.
What is the probability that you obtain a passing score, as a decimal rounded to 2 decimal places?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of combinations of things taken at a time and is calculated by !})
Since you know the answer to five of the questions, you are only concerned with the probability of guessing at least 9 out of 20 correctly (14 - 5 out of 25 - 5). Using the formula above, you need to calculate )
plus )
plus )
and so on up through )
, a total of 12 iterations of the formula.
\ =\ \sum_{k\,=\,9}^{20}\,\left[\left(20\cr k\right\)\left(0.2\right)^k\left(0.8\right)^{20\,-\,k}\right])
You can save yourself a little work by realizing that the probability of something happening is equal to 1 minus the probability of it not happening, which reduces the iterations of the formula to 9 instead of 12.
\ =\ 1\ -\ P_{20}(\leq{8},0.2)\ =\ 1\ -\ \sum_{k\,=\,0}^{8}\,\left[\left(20\cr k\right\)\left(0.2\right)^k\left(0.8\right)^{20\,-\,k}\right])
You can save yourself a ton of work by opening an Excel (or Numbers if you are on a Mac) spread sheet, picking a cell and typing:
})
Then hit "Enter" and say "Oh, no wonder I failed every time I've tried this."
John
My calculator said it, I believe it, that settles it
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