Answer:
See explanation ( Answers are too long)
Step-by-step explanation:
We will first compute a general probability for picking a white ball:
P (W) = a_1 / (a_1 + b_1) + a_2 / (a_2 + b_2) + a_3 / (a_3 + b_3)
part a)
We are asked to find the probability of white ball given that it pulled from bag A. So if we express it in notation we are asked for P ( A / W). We will use conditional probability to answer our question:
P ( A / W ) = P ( W & A ) / P (W)
P ( W & A ) = a_1 / (a_1 + b_1)
Hence,
P ( A / W ) = [a_1 / (a_1 + b_1)] / [a_1 / (a_1 + b_1) + a_2 / (a_2 + b_2) + a_3 / (a_3 + b_3)]
part b)
We are asked to find the probability of white ball given that it pulled from bag B. So if we express it in notation we are asked for P ( B / W). We will use conditional probability to answer our question:
P ( B / W ) = P ( W & B ) / P (W)
P ( W & B ) = a_2 / (a_2 + b_2)
Hence,
P ( A / W ) = [a_2 / (a_2 + b_2)] / [a_1 / (a_1 + b_1) + a_2 / (a_2 + b_2) + a_3 / (a_3 + b_3)]
part c)
We are asked to find the probability of white ball given that it pulled from bag C. So if we express it in notation we are asked for P ( C / W). We will use conditional probability to answer our question:
P ( C / W ) = P ( W & C ) / P (W)
P ( W & C ) = a_3 / (a_3 + b_3)
Hence,
P ( A / W ) = [a_3 / (a_3 + b_3)] / [a_1 / (a_1 + b_1) + a_2 / (a_2 + b_2) + a_3 / (a_3 + b_3)]
