kyanda17
  • kyanda17
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?
Mathematics
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SOLVED
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katieb
  • katieb
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dan815
  • dan815
hm
dan815
  • dan815
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)
anonymous
  • anonymous
Wait I just get k=4r-6...

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More answers

kyanda17
  • kyanda17
see i help u
anonymous
  • anonymous
Sorry, but it didn't help me much because I still can't figure it out :(
dan815
  • dan815
hey flyingpie
dan815
  • dan815
@flyingpie you see k has to be an interger from here and u know r is atleast 1
anonymous
  • anonymous
So the smallest is 10?
anonymous
  • anonymous
@dan815
dan815
  • dan815
can you take me to your question if u have other work up there i can see
anonymous
  • anonymous
@dan815 well at least 4 red because of problem statement, so 4(4)-6=10
anonymous
  • anonymous
Wait is k=4r-6 right @dan815
dan815
  • dan815
you cant really be sure, i need to see the rest of the work
dan815
  • dan815
you have to make sure that the solutions for white blue and green are also integers
anonymous
  • anonymous
4,3,2,1...
anonymous
  • anonymous
@dan815
dan815
  • dan815
again lol.. i cant confirm your answer without work xD
dan815
  • dan815
i mean u can just plug those values in and see if it is working out
anonymous
  • anonymous
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
anonymous
  • anonymous
It works but someone said that the answer is 21 from there packet...
dan815
  • dan815
ya there are infinite answers only 1 lowest
dan815
  • dan815
you can scale all the values up so that the probabilities still work out so
anonymous
  • anonymous
What do you think answer is @dan815
dan815
  • dan815
well im just going off by your statements, if u say u check it then 10 is the lowest i guess
dan815
  • dan815
(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)
dan815
  • dan815
http://prntscr.com/88hp94 looks like it is right
anonymous
  • anonymous
but could you tell me what is smallest possible? is it 10? Thanks!
anonymous
  • anonymous
@dan815
anonymous
  • anonymous
hello?

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