Question

A professor has learned that eight students in her class of 31 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam.

a. What is the probability that she finds at least one of the students cheating? (Round your final answers to 4 decimal places.)

b. What is the probability that she finds at least one of the students cheating if she focuses on eleven randomly chosen students? (Round your final answers to 4 decimal places.)

Answer 1

this is hypergeometric distribution with parameter:

sample size n=				10
population size N=				31
success population size k=				8

a)

probability =

P(X>=1)=

1-P(X<=0)=

1-∑x=0x-1     (kCx)(N-kCn-x)/(NCn) =

0.9742

b)

probability =

P(X>=1)=

1-P(X<=0)=

1-∑x=0x-1     (kCx)(N-kCn-x)/(NCn) =

0.9840