SOLUTION: can someone help me with these problems when you have a few min. thanks. Problem #1 Suppose you have three jars with the following contents: 2 black balls and 1 white ball in t

Question 86612: can someone help me with these problems when you have a few min. thanks.
Problem #1
Suppose you have three jars with the following contents: 2 black balls and 1 white ball in the first, 1 black ball and 2 white balls in the second, and 1 black ball and 1 white ball in the third. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. If
the probabilities of selecting the first, second, or third jar are 1/ 2, 1/ 3, and 1 /6, respectively,find the probabilities that if a white ball is drawn, it came from the following jars.
A) The third jar

Problem #2
Laura Johnson, a game show contestant, could win one of two prizes: a shiny new
Porsche or a shiny new penny. Laura is given two boxes of marbles. The first box has
50 pink marbles in it and the second box has 50 blue marbles in it. The game show
host will pick someone from the audience to be blindfolded and then draw a marble
from one of the two boxes. If a pink marble is drawn, she wins the Porsche. Otherwise,
Laura wins the penny.* Can Laura increase her chances of winning by redistributing
some of the marbles from one box to the other? Explain.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
================
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
=========
Cheers,
Stan H.

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