Question 1033050: A multiple choice test consists of seven questions, each of which has five choices. Each question has exactly one correct answer.
William guesses randomly at each answer. What is the probability that he gets five or fewer questions correct? (Round your answer to four 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:
\ =\ {{n}\choose{k}}\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 !})
You need to calculate the probability of 0 correct plus the probability of 1 correct plus the probability of 2 correct plus the probability of 3 correct plus the probability of 4 correct plus the probability of 5 correct. Symbolically:
\ =\ \sum_{k\,=\,0}^5\,{{7}\choose{k}}\left(0.2\right)^k\left(0.8\right)^{7\,-\,k})
Which is 6 probability calculations and 6 sums. Easier would be:
\ =\ 1\ -\ \sum_{k\,=\,6}^7\,{{7}\choose{k}}\left(0.2\right)^k\left(0.8\right)^{7\,-\,k})
calculating the probability of 6 correct plus the probability of 7 correct and then subtracting from 1. 2 probability calculations and 3 sums.
Easier yet, if you have access to Microsoft Excel on a PC or Numbers on a Mac, open a spreadsheet, pick a cell, and type:
=BINOMDIST(5,7,.02,TRUE)
When you hit enter, you get your answer.
John
My calculator said it, I believe it, that settles it
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