SOLUTION: A multiple choice test consists of five questions, each of which has four choices. Each question has exactly one correct answer.
William guesses randomly at each answer. What is
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Question 984389: A multiple choice test consists of five questions, each of which has four choices. Each question has exactly one correct answer.
William guesses randomly at each answer. What is the probability that he gets three 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 the probability of success on any individual trial is 
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 !})
Then the probability of less than or equal to successes (in other words successes or fewer), in trials with probability is:
\ =\ \sum_{i=0}^k\,{{n}\choose{i}}\left(p\right)^i\left(1\,-\,p\right)^{n\,-\,i})
You have some arithmetic to do. On the other hand, if you have Excel on your machine (or Numbers if you are using a Mac), open a spreadsheet and type:
)
And the spreadsheet will dutifully give you the answer to more decimal places than you could ever need as soon as you hit "Enter".
John
My calculator said it, I believe it, that settles it
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