SOLUTION: If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions:
What is the probability of getting AT LEAST 6 correct?
Algebra.Com
Question 1199510: If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions:
What is the probability of getting AT LEAST 6 correct?
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
The probability of exactly 
successes in 
independent trials with a uniform probability of success on any given trial of 
is given by:
\ =\ {{n}\choose{k}}\,(p)^k(1\,-\,p)^{n-k})
where 
is the number of combinations of things taken at a time.
The probability of at least successes in independent trials with a uniform probability of success on any given trial of is given by the sum:
\ =\ \sum_{r=k}^n\,{{n}\choose{r}}\,(p)^r(1\,-\,p)^{n-r})
Which is the probability of exactly successes plus the probability of exactly 
and so on up to the probability of exactly n successes.
Just plug in your numbers, remembering to express the probability as a decimal, and do the indicated arithmetic.
It may save you some arithmetic if you recognize that \ =\ 1\ -\ P(n,\leq\,k-1,p)\ =\ 1\ -\ \sum_{r=0}^{k-1}\,{{n}\choose{r}}\,(p)^r(1\,-\,p)^{n-r})
John
My calculator said it, I believe it, that settles it
From
I > Ø
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