SOLUTION: A multiple-choice test contains 12 questions, each with four answers. Assume a student just guesses on each question.
(Please enter your answers as fractions in simplest f
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Question 1131145: A multiple-choice test contains 12 questions, each with four answers. Assume a student just guesses on each question.
(Please enter your answers as fractions in simplest form or as decimals rounded to four decimal places.)
a. What is the probability that the student answers more than five questions correctly?
b. What is the probability that the student answers less than four questions correctly?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of exactly 
successes in 
trials where the probability of success on any given trial is 
is given by:
\ =\ {{n}\choose{k}}\,\(p\)^k\(1\,-\,p\)^{n-k})
The probability of at least successes in trials where the probability of success on any given trial is is given by:
\ =\ \sum_{r=k}^n\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n-r})
The probability of at most successes in trials where the probability of success on any given trial is is given by:
\ =\ \sum_{r=0}^k\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n-r})
Your number of trials is 12, and the probability of success on any trial is 1 in 4 or 0.25. Note that "more than 5" is the same as "at least 6", and "less than 4" is the same as "at most 3". You can do your own arithmetic.
John
My calculator said it, I believe it, that settles it
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