# Probability question on students

1. Oct 27, 2014

### tsukuba

1. The problem statement, all variables and given/known data
Each student who enters Professor James Moriarty's office has a 10% chance of being
manipulated in to 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

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

3. 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

2. Oct 27, 2014

### Dick

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?

3. Oct 27, 2014

### tsukuba

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

4. Oct 27, 2014

### tsukuba

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

5. Oct 27, 2014

### 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?

6. Oct 27, 2014

### Dick

"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.

7. Oct 27, 2014

### tsukuba

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