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help! probability question! probably combination problem!

knj9404

New member
Joined
May 1, 2012
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6
alright here's how it goes

there are 37 marbles in a box
3 of those 37 marbles are black marbles

what is the probability of a person taking out 5 marbles and one of those 5 marbles is a black marble?


my brain is about to burst
help plz
 

pka

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Jan 29, 2005
Messages
7,688
there are 37 marbles in a box
3 of those 37 marbles are black marbles
what is the probability of a person taking out 5 marbles and one of those 5 marbles is a black marble?
The probability that none of the five is black is \(\displaystyle \dfrac{\binom{34}{5}}{\binom{37}{5}}\).
So what is the probability that at least one of the five is black?
 

knj9404

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May 1, 2012
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to Pka

i think the problem is asking the probability when only one of the 5 marbles is black..
 

soroban

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Jan 28, 2005
Messages
5,588
Hello, knj9404!

The problem should have been given more precisely.
I will guess what you intended . . .


There are 37 marbles in a box: 3 of them are black marbles.
Five marbles are drawn out at random without replacement.
What is the probability that exactly one of those 5 marbles is black?

There are: .\(\displaystyle _{37}C_5\) possible outcomes.

There are: .\(\displaystyle \left(_3C_1\right)\left(_{34}C_4\right)\) outcomes with exactly one black marble.

\(\displaystyle P(\text{exactly 1 black marble}) \;=\;\dfrac{139,\!128}{356,\!643} \;=\;\dfrac{248}{777}\)
 

knj9404

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May 1, 2012
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Thank you Soroban!

your explanation helped a lot!
i think i get it now!

thank you so much for clear explanation!
 

pka

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Jan 29, 2005
Messages
7,688
i think the problem is asking the probability when only one of the 5 marbles is black..
Look at the OP.oes
there are 37 marbles in a box
3 of those 37 marbles are black marbles
Where in the OP statement does it say or even imply only one?
It does not!

The selection \(\displaystyle B.~B,~R\) contains a black ball.
 

knj9404

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May 1, 2012
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now i am confused pka

so what you are trying to tell me is that the question is elusive?
i think the question asks the possibility of one black marble in the 5 marbles that were drawn out of the box...

do you think it has a different solution to it?
 

pka

Elite Member
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Jan 29, 2005
Messages
7,688
so what you are trying to tell me is that the question is elusive?
i think the question asks the possibility of one black marble in the 5 marbles that were drawn out of the box...
do you think it has a different solution to it?
This is a simple matter of reading the English Language.
Suppose that we have a bin containing six black balls and five white balls.
Let's say that I reach in and get a handful of four balls.
The question is "do you have a black ball in hand"?

I have \(\displaystyle w,w,w,b\) so yes.

I have \(\displaystyle w,w,b,b\) so yes.

I have \(\displaystyle w,b,b,b\) so yes.

I have \(\displaystyle b,b,b,b\) so yes.

I have \(\displaystyle w,w,w,w\) so no!.

What is your problem with the English Language?
 

knj9404

New member
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May 1, 2012
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To pka

So the answer is still going to be 248/777?
because the question specifically does ask for a 'single' black ball
 
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