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1) A total of 46% of the voters in a certain city classify themselves as Independents, where as 30% classify themselves as Liberals and 24% say they are Conservatives. In s recent local election, 35% of the Independents, 62% of the Liberals and 58% of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, the probability that he or she is an Independent is _________ ans  0.331

2) A family has children with probability P_i where P1=0.01,P2=0.25,P3=0.35,P4=0.3. A child from this family is randomly chosen. Given that this child is the eldest child in the family, the conditional probability that the family has 4 children _______.ans  0.18

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Answer to 1st question :

Given , 

P(Independent)   =  0.46   =   r (say)

P(Liberal)   =   0.30       =    s

P(Conservative)   =  0.24   =  t

P(Vote | Independent)  =  0.35   =   u

P(Vote | Liberal)   =  0.62         =   v

P(Vote | Conservative)  =  0.58   =  w

So 

P(Independent | Vote)  =   ru / ( ru + sv + tw )

                                 =   (0.46 * 0.35) / [(0.46 * 0.35) + (0.3 * 0.62) + (0.24 * 0.58)]

                                 =    0.331

Hence the answer to the first question is 0.331

The second question has a bit lengthy calculation actually..

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