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kyanda17
 one year ago
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?
kyanda17
 one year ago
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?

This Question is Closed

dan815
 one year ago
Best ResponseYou've already chosen the best response.1let 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/(k1) * b/(k2)* g/(k3)= probability that each color is chosen (2) one white, one blue, and two reds are chosen, w/k * b/(k1)*r/(k2)*(r1)/(k3) you can do these (3) (4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait I just get k=4r6...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, but it didn't help me much because I still can't figure it out :(

dan815
 one year ago
Best ResponseYou've already chosen the best response.1@flyingpie you see k has to be an interger from here and u know r is atleast 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the smallest is 10?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1can you take me to your question if u have other work up there i can see

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 well at least 4 red because of problem statement, so 4(4)6=10

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait is k=4r6 right @dan815

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you cant really be sure, i need to see the rest of the work

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you have to make sure that the solutions for white blue and green are also integers

dan815
 one year ago
Best ResponseYou've already chosen the best response.1again lol.. i cant confirm your answer without work xD

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i mean u can just plug those values in and see if it is working out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0work: the probabilities have same denominator, but the numerators are rwbg=rwb(r1)=r(r1)(r2)b=r(r1)(r2)(r3), so g=r1, w=r2, b=r3, and k=r+w+b+g=4r6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It works but someone said that the answer is 21 from there packet...

dan815
 one year ago
Best ResponseYou've already chosen the best response.1ya there are infinite answers only 1 lowest

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you can scale all the values up so that the probabilities still work out so

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What do you think answer is @dan815

dan815
 one year ago
Best ResponseYou've already chosen the best response.1well im just going off by your statements, if u say u check it then 10 is the lowest i guess

dan815
 one year ago
Best ResponseYou've already chosen the best response.1(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*(r1) = b*r*(r1)*(r2)=r*(r1)(r2)(r3)

dan815
 one year ago
Best ResponseYou've already chosen the best response.1http://prntscr.com/88hp94 looks like it is right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but could you tell me what is smallest possible? is it 10? Thanks!
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