SOLUTION: a student takes a 22 question multiple choice exam with four choices for each question and guesses on each question. Assume the variable is binomial find the probability of guessin
Algebra.Com
Question 1127552: a student takes a 22 question multiple choice exam with four choices for each question and guesses on each question. Assume the variable is binomial find the probability of guessing at least 7 out of 22 correctly
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need the probability of seven successes out of 22 trials, plus eight successes out of 22 trials, plus nine...and so on up to 22 successes out of 22 trials.
The probability of 
successes out of 
trials where the probability of success on any given trial is 
is given by:
\ =\ {{n}\choose{k}}\,\(p\)^k\(1\,-\,p\)^{n\,-\,k})
So you need the sum:
\ =\ \sum_{r=k}^n\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n\,-\,r})
For at least 7 out of 22, you will have a sum with 16 terms. The following sum, which gives you the same result only requires calculating 8 terms:
\ =\ 1\ -\ P\(<k,n,p\)\ =\ 1\ - \sum_{r=0}^k\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n\,-\,r})
Make sure your calculator has fresh batteries.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
a student takes a 20 question multiple choice exam with 5 choices for each question and... (answered by stanbon)
a student takes a 8- question, multiple-choice exam with 2 choices for each question and... (answered by stanbon)
A student takes a 10-question, multiple-choice exam with three choices for each question... (answered by Edwin McCravy)
A student takes a 10-question, multiple-choice exam with three choices for each question... (answered by Fombitz)
A student takes a 4-question, multiple-choice quiz with 3 choices for each question. If... (answered by mathmate)
A student takes a 20-question, multiple choice exam with five choices for each question... (answered by stanbon)
A student takes a 4 question multiple choice quiz with 4 choices for each question. If... (answered by stanbon)
a student takes a 4 question multiple choice quiz with 4 choices for each question. IF... (answered by stanbon)
A student takes a 5 question multiple choice quiz with 4 choices for each question. If... (answered by Fombitz)