Each of three bags A, B, C contains white balls and black balls. A has a1 white & b1 black, B has a2 white & b2 black and C has a3 white & b3 black. A ball is drawn at random and is found to be white. Find the respective probability that it is from A, B & C.

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)]    

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.