# help! probability question! probably combination problem!

#### knj9404

##### New member
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

##### Elite Member
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

##### New member
to Pka

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

#### soroban

##### Elite Member
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

##### New member
Thank you Soroban!

i think i get it now!

thank you so much for clear explanation!

#### pka

##### Elite Member
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

##### New member
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
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
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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