Calculate a probability someone will do the same N tasks from X tasks as you

M

MatejR

New member
Joined
Mar 18, 2020
Messages
6
Hello! Newcomer here!

I need a little bit of a help for a certain task.

Task is as follows: from 30 tasks, you have to choose 8 of them (any order). What is the probability someone will from a class of 24 students choose the SAME 8 TASKS AS YOU DID?

I tried doing 30C8 to get all of the possible combinations someone can get by choosing 8 tasks from those 30 tasks and then 24C8 to get all of the possible combinations students can pick. Then I divide 24C8 by 30C8 to get that probability.

I sadly do not have a solution to this, but I have a feeling I made a mistake somewhere.

Any help/feedback is appriciated!
 
Choose your tasks. Now you first want to find the probability that anyone selects the same combination of tasks.

This is simply [MATH]p_1 = \dfrac{1}{\dbinom{30}{8}}[/MATH]
Now how many of these classmates select the same combo of tasks has a binomial distribution with parameters
[MATH]n=24,~p=p_1[/MATH]
You are looking for [MATH]P[k\geq 1] = 1 - P[k=0][/MATH]
can you finish?
 
Romsek said:
Choose your tasks. Now you first want to find the probability that anyone selects the same combination of tasks.

This is simply [MATH]p_1 = \dfrac{1}{\dbinom{30}{8}}[/MATH]
Now how many of these classmates select the same combo of tasks has a binomial distribution with parameters
[MATH]n=24,~p=p_1[/MATH]
You are looking for [MATH]P[k\geq 1] = 1 - P[k=0][/MATH]
can you finish?
Click to expand...

Nope. This is my first time seeing binomial distribution with parameters.
 
MatejR said:
Nope. This is my first time seeing binomial distribution with parameters.
Click to expand...

What did you see when you saw the binomial distribution before? You need both those parameters.
Take a look at the wiki page on it.
 
Romsek said:
What did you see when you saw the binomial distribution before? You need both those parameters.
Take a look at the wiki page on it.
Click to expand...

OOH those parameters are N and K. I thought it was something else, my bad.

But I have no idea how I would solve the equation (P[k≥1]=1−P[k=0]) you wrote. I see this kind of format for the first time.
 
And to be sure, [MATH](1/30C8)[/MATH] is the formula to calculate the probability of those 24 students, 1 chooses the same 8 tasks as me?
 
Last edited:
MatejR said:
And to be sure, [MATH](1/30C8)[/MATH] is the formula to calculate the probability of those 24 students, 1 chooses the same 8 tasks as me?
Click to expand...

That is the probability that a single classmate chooses the same 8 tasks as you.

And no, K does not correspond to p. You need to go read your text again about the binomial distribution.
 
Romsek said:
And no, K does not correspond to p. You need to go read your text again about the binomial distribution.
Click to expand...

I will sadly then have a problem with solving this part.
 
Last edited:
Binomial distribution(n,p)

[MATH]p[k] = \dbinom{n}{k}p^k(1-p)^{n-k}[/MATH]
Do you think you can plug the parameters above and k=0 into that?
 
You must log in or register to reply here.
Top