Question 1161372
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I'm not sure what help you need with this... unless you are just looking for somebody to do your work for you.<br>
The process for finding the answers is straightforward; but it requires some effort.<br>
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.<br>
(a) Find the probability of getting 2 blue followed by 2 purple....<br>
first draw:
contents 5 blue and 7 purple; P(blue) = 5/(5+7) = 5/12
return the blue plus 2 more blue<br>
second draw:
contents 7 blue and 7 purple; P(blue) = 7/(7+7) = 7/14 = 1/2
return the blue plus 2 more blue<br>
third draw:
contents 9 blue and 7 purple; P(purple) = 7/(9+7) = 7/16
return the purple plus 2 more purple<br>
fourth draw:
contents 9 blue and 9 purple; P(purple) = 9/(9+9) = 9/18 = 1/2<br>
P(B,B,P,P) = (5/12)(1/2)(7/16)(1/2) = 35/768<br>
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<br>
Analyze those 5 cases as shown for the case BBPP and add the probabilities of all 6 cases....<br>