Question

The Nervous System (BIOM A632) is currently being taught by Dr. Hinterberger at UAA. Dr. Hinterberger decided to give a short quiz of 10 questions; each question has four possible answers. What is the probability of getting two incorrect answers? (Use Binomial Table)

Answer 1

Solutions
Given:
n= 10
Each question has four possible answers.

therefore possibility of correct answer is 1/4
Let p be the probability of correct answer and q be the probability of incorrect answer.
p=1/4=0.25
q= 1-p = 0.75
Let X be binomial random variable which denotes number of correct answer.
X~ binomial distribution (n=10,p=0.25)
The pmf of the binomial random variable is given by
P(X=x)= (nCx) (p^x) [q^(n-x)] , where q=1-p
=(10Cx)(0.25^x) [0.75^(10-x)]
P(getting two incorrect answers)= 1- P(getting eight correct answers)
=1-P(X=8)
=1-{(10C8)(0.25^8) [0.75^(10-8)]}
=1- {(45)(0.25^8)(0.75^2)}
=1- (0.0004)
= 0.9996
P(getting two incorrect answers) = 0.9996