SOLUTION: I appreciate any help I can get on this chance experiment problem. Please Help! Jar of marbles initially contains 5 blue and 7 purple balls. Each time a marble is drawn, the col

Question 1161372: I appreciate any help I can get on this chance experiment problem. Please Help!
Jar of marbles initially contains 5 blue and 7 purple balls. Each time a marble is drawn, the color is noted and it is then replaced in jar urn along with 2 other balls of the same color (for example, John draws a blue marble on draw one, then places the blue marbles he selected along with two other blue marbles back in the jar).
a. What is the probability that the first 2 marbles drawn by John are blue and the next 2 are purple?
b. What is the probability that of the first 4 marbles drawn, exactly 2 are blue?

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I'm not sure what help you need with this... unless you are just looking for somebody to do your work for you.

The process for finding the answers is straightforward; but it requires some effort.

I'll answer part (a) for you. The answer for part (b) will be found in the same way; but it requires analyzing many different cases. Our time as tutors is not well spent doing that, since the process is always the same. You will need to do that tedious work yourself.

(a) Find the probability of getting 2 blue followed by 2 purple....

first draw:
contents 5 blue and 7 purple; P(blue) = 5/(5+7) = 5/12
return the blue plus 2 more blue

second draw:
contents 7 blue and 7 purple; P(blue) = 7/(7+7) = 7/14 = 1/2
return the blue plus 2 more blue

third draw:
contents 9 blue and 7 purple; P(purple) = 7/(9+7) = 7/16
return the purple plus 2 more purple

fourth draw:
contents 9 blue and 9 purple; P(purple) = 9/(9+9) = 9/18 = 1/2

P(B,B,P,P) = (5/12)(1/2)(7/16)(1/2) = 35/768

To answer part (b), there are 5 other ways you can get 2 blue and 2 purple in the first 4 draws:
BPBP
BPPB
PBBP
PBPB
PPBB

Analyze those 5 cases as shown for the case BBPP and add the probabilities of all 6 cases....

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