help with this simple probability problem

[fallen island]

There are a total of 48 students in a class. Twenty are boys and 28 are girls.

If a committee of 3 students is formed, what is the probability that
a. all are girls? b. two are boys and one is a girl?

[turbid copper]

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[shrewd jetty]

You can use hypergeometric distribution here.

[lavish gale]

Use permutations and combinations and solve it

[fallen island]

Holdon I don't know that yet, I'm on the very basic level of probability

[gentle pier]

28/48×27/47×26/46

[deep socket]

tf

[gentle pier]

Here you multiply the variables like I did

[fallen island]

Yess feed me with thy knowledge

Educate me more

[gentle pier]

Cause probably is multiplied when you are taking 2 or more cases

[tender scroll]

a is 9.3/16?

idk

[gentle pier]

This this case you multiply the probability thrice

[fallen island]

Do you mean independent events

[gentle pier]

Yep

[fallen island]

My answer is way off I used combination

[shrewd jetty]

Ah, no problem.
Suppose you have N objects, D of which are marked.
You take a sample of n objects. Then the number X of marked objects in the sample follows a hypergeometric distribution: X ~ HG(N, D, n).
Its PMF is:
P(X = k) = C(D, k) C(N - D, n - k)/C(N, n)
Here C(n, k) = n!/(k! (n - k)!) is the binomial coefficient.

[gentle pier]

And probability formula is p(x)=no of favorable outcomes /total number of outcomes

[lavish gale]

Yessir that's how u solve it

[tender scroll]

what is the answer anyways

[lavish gale]

The probability of picking a boy in the class will be 5/12 and for girls it'll be 7/12

[gentle pier]

Favorable outcomes start with 28 and total outcomes start with 48

[lavish gale]

Yup

[fallen island]

Lmfao my stupid ass got 3276/17296 simplified to 819/4324

[lavish gale]

Howd you even get that 😭

[fallen island]

I dont know what I'm doing 😭😭

[lavish gale]

Did you simplify the permutation

[fallen island]

C(28,3)/C(48,3)

[shrewd jetty]

Is this for (a)?

[fallen island]

Yes

[shrewd jetty]

Alright, nice!

[fallen island]

Am I hopeless

[shrewd jetty]

And for (b)?

[lavish gale]

Probability of all 3 community members being girls is given by 28C3/48C3

[fallen island]

Uhhm let me check

[lavish gale]

2 boys one girl would be

[shrewd jetty]

Let Scepter try first.

[lavish gale]

20C3 x 28C3/ 48C3

[lavish gale]

yeah my bad

[shrewd jetty]

Well, that's incorrect, anyway.

[gentle pier]

I'm getting 0.189407955596669 for a

[shrewd jetty]

Use ordinary fractions.

[lavish gale]

Damn

[gentle pier]

I used a calculator

[shrewd jetty]

Well, then don't.

[fallen island]

It's C(20, 2) × C(28, 1) / C(48, 3)

[shrewd jetty]

Nice!

[lavish gale]

Ye

[shrewd jetty]

Now, just simplify both answers a bit. The numbers aren't too big, so you can do it by hand.

[fallen island]

plugs it in on a fraction calculator

[shrewd jetty]

No, don't use a calculator.

[fallen island]

Okay thanks y'all for helping

Time to find another problem

[shrewd jetty]

You're welcome!

I recommend learning about some common distributions.

[fallen island]

+close