Question 86612
1st Problem:

p(3rd jar|white)
=[P(3rd jar and white)/P(w)
=[(1/6)*(1/2)]/]P(white and 1st)+P(white and 2nd)+P(white and 3rd)]
=[1/12]/[(1/2)(1/4)+(1/3)(2/3)+(1/6)(1/2)]
= [1/12]/[31/72] 
= 6/31
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2nd Problem:

As it stands her chances of winning are 1/2
If she changes the mixture to Jar1 with x pink and 50-x white and Jar2 with 50-x pink  and and x white, the probability of pink is still 
(1/2)(x/50) + 1/2(50-x)/50
= (1/2)[x/50 + (50-x)/50]
= 1/2 [ (50x+2500-50x)/2500] = (1/2)(1) = 1/2
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Cheers,
Stan H.