SOLUTION: A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the
Algebra.Com
Question 320257: A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the probability of getting exactly 5 correct answers?
b. What is the probability of getting less than 6 correct answers?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Part a. You want the probability of 
successes out of 
trials where the probability of success on any given trial is 
.
\ =\ \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 computed by !})
.
For this particular problem:
and
Hence you need to calculate:
\ =\ \left(15\cr \,5\right\)\left(\frac{1}{4}\right)^5\left(\frac{3}{4}\right)^{10})
where )
is the number of combinations of 
things taken 
at a time and is computed by !})
.
I'll leave the calculator work to you.
Part b. The probability of getting less than 6 correct is the sum of the probability of getting exactly 0 plus exactly 1 plus...plus exactly 5. In other words:
\ =\ \sum_{k=0}^5\left(15\cr \,k\right\)\left(\frac{1}{4}\right)^k\left(\frac{3}{4}\right)^{15\ -\ k})
Again, I'll leave the calculator work to you.
John
RELATED QUESTIONS
A multiple choice test has 20 questions with each having 4 possible answers with one... (answered by stanbon)
A Multiple-choice test has 15 questions with each having 4 possible answers with one... (answered by stanbon)
A multiple choice test has 20 questions with each having 4 possible answers with one... (answered by stanbon)
I need help in this question. I know that n=15 and p=0.2 and q=0.8. But don't quite... (answered by drk)
Please help.
A test consist of 15 multiple choice questions, with each questions... (answered by ikleyn)
An unprepared student randomly circles answers in a multiple choice test having 25... (answered by stanbon)
Assume that the test has 8 true/false questions, and 11 multiple choice questions (4... (answered by Glaviolette)
1. A student randomly answers the 7 questions on a multiple choice test.
Each... (answered by Edwin McCravy)
I understand basic probability but am very confused when it comes to the below question. (answered by stanbon,solver91311)