Question

If a committee with 2 student members is to be formed, what is the probability of forming a committee with one A grade student and one F grade student?

if a committee with 3 student members is to be formed, what is the probability of forming a committee with two A grade student and one B grade student?

If the records show that, the probability of failing (with grade F) this course is p,[use the answer of question previous( 0.0666) , p, here ],what is the probability that at most 2 students out of 15 fail this course? {Hint: use binomial distribution

Chart grades and students

A:10

B:2

C:2

D:0

F:1

Answer 1

1)

probability of forming a committee with one A grade student and one F grade student

=(10C1)*(1C1)/(15C2) =10*1/105 =2/21

2)

probability of forming a committee with two A grade student and one B grade student

=(10C2)*(2C1)/(15C3)

=45*2/455

-18/91

3)

probability that at most 2 students out of 15 fail this course =P(X=0)+P(X=1)+P(X=2)

=(15C0)*(0.0666)^0*(1-0.0666)^15+(15C1)*(0.0666)^1*(1-0.0666)^14+(15C2)*(0.0666)^2*(1-0.0666)^13

=0.9264