SOLUTION: A student takes a 20-question, true/false exam and guesses on each question. fkind the probability of passing if the lowest passing grade is 15 correct out of 20. How do I comput
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Question 316540: A student takes a 20-question, true/false exam and guesses on each question. fkind the probability of passing if the lowest passing grade is 15 correct out of 20. How do I compute using the binomial distribution formula:
P(X) = n! *p
_______
(n-x)!X!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The basic formula for the probability of exactly 
successes out of 
trials where the probability of a successful outcome on a single trial is fixed at 
is given by:
\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of combinations of things taken at a time and is calculated by:
\ =\ \frac{n!}{k!(n\ -\ k)!})
But you need the probability of 15 right answers plus 16 right answers plus ... plus 19 right answers plus 20 right answers.
So you need:
\ =\ \sum_{i=15}^{20}\left(20\cr \ i\right\)0.5^i\left(1\,-\,0.5\right)^{n\,-\,i}\ =\ \sum_{i=15}^{20}\left(20\cr \ i\right\)0.5^i\left(0.5\right)^{n\,-\,i}\ )
But since ^{n\,-\,i}\ =\ 0.5^n)
, we can write:
\ =\ \left(\left(20\cr 15\right\)+\ \left(20\cr 16\right\)\ +\left(20\cr 17\right\)\ +\left(20\cr 18\right\)\ +\left(20\cr 19\right\)\ +\left(20\cr 20\right\)\right)0.5^{20})
Get busy. You have some serious calculator punching to do. Or you can use Excel. The formula: =COMBIN(N,K) where N and K are the values you want gives you the value of
I ran this out and got a little over 2% probability.
SUPER-DOOPER DOUBLE PLUS EXTRA CREDIT.
10 question multiple-choice exam. All questions have four possible responses. Passing grade is 6 or better correct. Probability you can pass by just guessing?
John
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