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

MatejR

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Mar 18, 2020
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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?
 
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?

Nope. This is my first time seeing binomial distribution with parameters.
 
Nope. This is my first time seeing binomial distribution with parameters.

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.
 
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.

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?
 
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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?

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

I will sadly then have a problem with solving this part.
 
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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?
 
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