Probability question on students

[tsukuba]

Homework Statement

Each student who enters Professor James Moriarty's office has a 10% chance of being
manipulated into participating in some criminal scheme. Assume that Moriarty's classes are so
large that the students can be considered independent with regard to their meetings with him.
If 18 students visit Moriarty during his office hours, then the probability he will gain four or
more new criminal underlings is

Homework Equations

I am 100% sure this a binomial random variable.
the formula is:
p(x)= nCx * p^x * (1-p)^n-x

The Attempt at a Solution

so n=18
x=0,1,2,3
p=0.1

p(x=0)=0.15
p(x=1)=0.017
p(x=2)=1.85x10^-3
p(x=3)=2.06x10^-4

p(4 or more students)= 1- p(x=0) - p(x=1) - p(x=2) - p(x=3)
=0.831

The answer is 0.098

 

[Dick]

Homework Statement

Each student who enters Professor James Moriarty's office has a 10% chance of being
manipulated into participating in some criminal scheme. Assume that Moriarty's classes are so
large that the students can be considered independent with regard to their meetings with him.
If 18 students visit Moriarty during his office hours, then the probability he will gain four or
more new criminal underlings is

Homework Equations

I am 100% sure this a binomial random variable.
the formula is:
p(x)= nCx * p^x * (1-p)^n-x

The Attempt at a Solution

so n=18
x=0,1,2,3
p=0.1

p(x=0)=0.15
p(x=1)=0.017
p(x=2)=1.85x10^-3
p(x=3)=2.06x10^-4

p(4 or more students)= 1- p(x=0) - p(x=1) - p(x=2) - p(x=3)
=0.831

The answer is 0.098

The idea is correct, but I don't think the numbers you are getting for p(x=1), p(x=2) and p(x=3) look correct. Can you show the arithmetic you did you get p(x=1) some of them?

 

[tsukuba]

p(x=1)= 18C1 * 0.1^1 * 0.9^17

 

[tsukuba]

yes, I figured out what I did wrong with my numbers. I will try the question with the correct numbers now.

 

[tsukuba]

hey I got the answer! thanks for pointing out my math was wrong.
:)

I have another question though..
for that question it stated 4 or more.. so I did 1- the addition of 0,1,2,3
Lets say it said "at least 4"
would I just have to add 0,1,2,3 and that'll be my answer?

 

[Dick]

hey I got the answer! thanks for pointing out my math was wrong.
:)

I have another question though..
for that question it stated 4 or more.. so I did 1- the addition of 0,1,2,3
Lets say it said "at least 4"
would I just have to add 0,1,2,3 and that'll be my answer?

"At least 4" means the same thing as "4 or more", doesn't it? If you mean "at most 4" you'd have to add 0,1,2,3,4.

 

[tsukuba]

haha yea sorry..
and alright got it! thank you