Probability question on students

In summary, the probability of Professor James Moriarty gaining four or more new criminal underlings out of 18 students who visit his office hours is 0.831. This can be calculated using the binomial random variable formula, where p(x) is equal to nCx * p^x * (1-p)^n-x. In this case, n is 18, x can be 0, 1, 2, or 3, and p is 0.1. The probability of gaining exactly 0, 1, 2, or 3 new criminal underlings can be calculated using this formula, and then the probability of gaining 4 or more can be found by subtracting the sum of these
  • #1
tsukuba
47
0

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
 
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  • #2
tsukuba said:

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?
 
  • #3
p(x=1)= 18C1 * 0.1^1 * 0.9^17
 
  • #4
yes, I figured out what I did wrong with my numbers. I will try the question with the correct numbers now.
 
  • #5
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
tsukuba said:
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.
 
  • #7
haha yea sorry..
and alright got it! thank you
 

1. What is the definition of probability?

Probability is a measure of the likelihood that a certain event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How is probability used in statistics?

Probability is used in statistics to analyze and interpret data, make predictions, and test hypotheses. It helps us understand the chances of certain outcomes and make informed decisions.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumptions, while experimental probability is based on actual data from experiments or observations. Theoretical probability is often used to predict outcomes, while experimental probability is used to validate or test those predictions.

4. How can probability be applied in a classroom setting?

In a classroom, probability can be used to teach students about chance and uncertainty, and how to make decisions based on data. It can also be used to design and conduct experiments, and to analyze and interpret results.

5. What are some common misconceptions about probability among students?

Some common misconceptions about probability among students include the belief that all outcomes are equally likely, that past events can influence future outcomes, and that probability can be determined by intuition or gut feelings. It is important to address these misconceptions and help students develop a more accurate understanding of probability.

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