Question

A boy takes 12 ink cartridges down from a shelf. Three of them do not have any ink. When selecting four out of the 12, what is the pobability of getting one without ink.

Answer 1

\[P(1)=\frac{\left(\begin{matrix}3 \\ 1\end{matrix}\right)\left(\begin{matrix}9 \\ 3\end{matrix}\right)}{\left(\begin{matrix}12 \\ 4\end{matrix}\right)}\]

Answer 2

Thank you for showing me how to figure it out .

Answer 3

i will teach youu

Answer 4

now the question says 3 of them do not have ink so how many have ink?

Answer 5

You're welcome :) Do you know how to calculate the binomial coefficients?

Answer 6

No

Answer 7

hey you answer me I Wwanna teach :)

Answer 8

\[\left(\begin{matrix}n \\ r\end{matrix}\right)=\frac{n!}{r!(n-r)!}\]

Answer 9

got it, thank you. Now maybe I'll be able to finsh my homework. Have a great weekend and thank you again.

Answer 10

You're welcome :)

Answer 11

kropot!!

Answer 12

what are all those notations

Answer 13

The solution can also be expressed as
\[P(1)=\frac{3C1\times 9C3}{12C4}\]

Answer 14

i dont understand those Cs nad Ps is my calcuation the same thing as that?

Answer 15

how are u thinking about this question ?

Answer 16

4*(3/12*9/11*8/10*7/9 i mean that

Answer 17

4*(3/12*9/11*8/10*7/9) = 51% ish

Answer 18

@dan815 If you calculation is
\[4(\frac{4}{12}\times \frac{9}{11}\times \frac{8}{10}\times \frac{7}{9})=0.67879\]
then it is not correct.

Answer 19

4/12 to 3/12

Answer 20

cuz 4 + 9 = 13, 1 more than there shud be xD

Answer 21

@dan815 Your amended calculation gives the correct answer.

Answer 22

can you tell me how you get the same answer with Cs and Ps though
this is how i did it
___,___,___,___ 4 spots and probability of getting noncolor = 3/12 and the other spots are 9/11,8/10,7/9 so the noncolor can be in 4 spots so
4*(3/12*9/11*8/10*7/9) = solution
is that basically what ur doing with C and P formula

Answer 23

I have used the hypergeometric distribution that treats sampling without replacement. It appears that you are basically using the same.

Answer 24

r u some genius??

Answer 25

Not really. Just a student :)

Answer 26

so then how did u solve what i needed like 3 lines off work in 1 division sign

Answer 27

There was much the same work in calculating the binomial coefficients and then multiplying and dividing them as in your calculation. I have left the detailed calculations to the questioner who says they understand what to do.

Answer 28

i think im staring to understand what u did
so basically you said for a situation where there are 4 spots 3 without color go to 1 spot and 9 with color go to 3 spots and then divided by all the possibile situations with those 4 spots are 12 into 4 spots

Answer 29

so
p(2) = (3C2)*(9C2)/(12C4)

Answer 30

@dan815 Your equation for p(2) is correct.