Question

Twelve balls are kept in 3 boxes. Find the probability that first box contains 3 balls.

Answer 1

@asnaseer

Answer 2

I would work out how many balls can be in the first box and then work out the probability of getting exactly 3 in the first box.

e.g. the first box could contain 1 ball and the other two would then contain 11 between them. so I would create a table like this:

first box other boxes
------- ----------
1 11
2 10
...

Answer 3

so what is the maximum number of balls you could have in the first box such that the other two boxes also contain at least one ball?

Answer 4

(one ball each that is)

Answer 5

what will be the sample space in this question??

Answer 6

it tells you that there are 12 balls all together

Answer 7

12C3...for 3 boxes are also there...would it be the sample space??

Answer 8

I'm not sure what you are getting at Mitul?

Answer 9

if you just fill out that table I started above, then the answer should become obvious

Answer 10

but then how will it go about...i mean for each box to have atleast one ball...box 1 should contain 10 balls...
then what?

Answer 11

i want 3 balls in box 1

Answer 12

so now you know that box 1 can contain between 1 to 10 balls

Answer 13

yup... but what will be its mathematical interpretation?

Answer 14

now for each row of that table - you just need to calculate the number of combinations that the remaining balls can take into boxes 2 and 3.

e.g. for the first row, we have 1 ball in box 1 and 11 in the other 2. So how many ways are there of distributing 11 balls between 2 boxes such that each one has at least one ball in it?

Answer 15

53 ways ..i guess

Answer 16

I get 10 ways

Answer 17

1 and 10
2 and 9
...
10 and 1

Answer 18

but it will be 53 ways since 11 balls can be kept in 2 boxes in 11 C 2 ways and minusing the event that each of them once has no ball in it, we get 53 ways..

Answer 19

there is probably a far simpler /mathematical/ way of doing this problem but I'm not familiar enough with this topic.

Answer 20

I can't see more than 10 ways - the ones I listed above.

Answer 21

okkk. if it is the way u r telling wat will the answer be??

Answer 22

I haven't worked through the whole problem. you need to calculate the combinations for each row, then see what proportion of the row with 3 balls in it is if the total to get the answer.

Answer 23

I think it will come out at something like 8/55

Answer 24

not the answer...do u know any good book for probability?

Answer 25

sorry :(
out of interest - what is the right answer?

Answer 26

220*(2^9/3^21)

Answer 27

O.O

Answer 28

ok - I think I know some users who may be able to help here, I'll mention them so that they can take a look when they are online.

Answer 29

@KingGeorge @Zarkon @joemath314159 @JamesJ can you please assist this user with probability?

Answer 30

kk thanks anyways...u have been of great help @asnaseer

Answer 31

yw :)

Answer 32

@Mitul Are you saying the answer is
\[220\times \frac{2^{9}}{3^{21}}\]

Answer 33

yup

Answer 34

Have you calculated the value of 3^21?

Answer 35

The sample space is 55 ways of distributing the balls between the 3 boxes with at least 1 ball in every box. 8 of the 55 ways have 3 balls in the first box. So the answer by @asnaseer 8/55 is correct,

Answer 36

donno....maybe then my book will be wrong...thanks for the help @kropot72

Answer 37

You're welcome :)

Answer 38

thanks for checking this @kropot72 - I was beginning to doubt my sanity :)

Answer 39

@asnaseer Glad to be of help :)