Question

A bag contains some marbles, each of which is one of four colors (red, white, blue, and green). At least one of the marbles is red. The composition of the bag is such that if we take four marbles out at random (without replacement), each of the following is equally likely:

(1) one marble of each color is chosen,

(2) one white, one blue, and two reds are chosen,

(3) one blue and three reds are chosen,

(4) four reds are chosen.

What is the smallest possible number of marbles in the bag?

Answer 1

hm

Answer 2

let r,w,b,g equal the number of red,white,blue green marbles respectively
let k = r+w+b+g, k is the total number of marbles

(1) 1 marble of each color is chosen
r/k * w/(k-1) * b/(k-2)* g/(k-3)= probability that each color is chosen

(2) one white, one blue, and two reds are chosen,
w/k * b/(k-1)*r/(k-2)*(r-1)/(k-3)

you can do these
(3)

(4)

Answer 3

Wait I just get k=4r-6...

Answer 4

see i help u

Answer 5

Sorry, but it didn't help me much because I still can't figure it out :(

Answer 6

hey flyingpie

Answer 7

@flyingpie you see k has to be an interger from here and u know r is atleast 1

Answer 8

So the smallest is 10?

Answer 9

@dan815

Answer 10

can you take me to your question if u have other work up there i can see

Answer 11

@dan815 well at least 4 red because of problem statement, so 4(4)-6=10

Answer 12

Wait is k=4r-6 right @dan815

Answer 13

you cant really be sure, i need to see the rest of the work

Answer 14

you have to make sure that the solutions for white blue and green are also integers

Answer 15

4,3,2,1...

Answer 16

@dan815

Answer 17

again lol.. i cant confirm your answer without work xD

Answer 18

i mean u can just plug those values in and see if it is working out

Answer 19

work: the probabilities have same denominator, but the numerators are rwbg=rwb(r-1)=r(r-1)(r-2)b=r(r-1)(r-2)(r-3), so g=r-1, w=r-2, b=r-3, and k=r+w+b+g=4r-6

Answer 20

It works but someone said that the answer is 21 from there packet...

Answer 21

ya there are infinite answers only 1 lowest

Answer 22

you can scale all the values up so that the probabilities still work out so

Answer 23

What do you think answer is @dan815

Answer 24

well im just going off by your statements, if u say u check it then 10 is the lowest i guess

Answer 25

(1) one marble of each color is chosen,
(2) one white, one blue, and two reds are chosen,
(3) one blue and three reds are chosen,
(4) four reds are chosen.
k=r+w+g+b
rwgb = wbr*(r-1) = b*r*(r-1)*(r-2)=r*(r-1)(r-2)(r-3)

Answer 26

http://prntscr.com/88hp94 looks like it is right

Answer 27

but could you tell me what is smallest possible? is it 10? Thanks!

Answer 28

@dan815

Answer 29

hello?