SOLUTION: A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the

Question 1102406: A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60 %.
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Each question has a 0.25 probability of being right
Want 12 or more right
start with 12, 20C12(0.25^12)(0.75^8)=0.0008
20C13*0.25^13*0.75^7=0.0002-- both are 0.0009 if the rounding is done only at the end.
20C14*0.25^14*0.75^6=0.000026
Probability is 0.0009
Expected value is 5, np, and variance is 5(.75)=3.75, so sd is sqrt (3.75)=1.94, so this is about 3.5 sd s from mean of 5.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
To get 60%, the person needs to get 12 answers correct(0.60 * 20)
:
probability(p) of guessing correctly on a problem is 1/4 = 0.25
:
we use the binomial probability formula
:
Probability (k successes out of n trials) = nCk * p^k * (1-p)^(n-k), where p is probability of a success, nCk = n! / (k! * (n-k)!)
:
for this problem n=20, k=12, p = 0.25
:
P (12 successes out of 20 trials) = 20C12 * (0.25)^12 * (1-0.25)^(20-12) = 0.00075
:
*************************************************************
Probability of getting 60% on the quiz by guessing is 0.00075
:
good reason to study :-)
*************************************************************
:
RELATED QUESTIONS
A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For... (answered by stanbon)
A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For... (answered by drk)
A quiz consists of 20 multiple-choice questions, each with 4 possible answers. For... (answered by ikleyn,math_tutor2020)
A quiz consists of 20 multiple-choice questions, each with 6 possible answers. For... (answered by stanbon)
A quiz consists of 20 multiple-choice questions, each with 5 possible answers. For... (answered by ewatrrr)
(1 point) A quiz consists of 10 multiple-choice questions, each with 4 possible answers.... (answered by ikleyn)
A quiz cosists of 20 multiple-choice questions, each with 4 possible answers. For someone (answered by stanbon)
A quiz consists of 10 multiple-choice questions, each with 5 possible answers. For... (answered by stanbon)
A quiz consists of 10 multiple-choice questions, each with 6 possible answers. For... (answered by reviewermath)