A.1 Urn A contains 3 red and 5 black balls, whereas urn B contains 6 reds and 4

Question

A.1 Urn A contains 3 red and 5 black balls, whereas urn B contains 6 reds and 4 white balls. a) f a bal is randomly selected and found to be red, what is the probability that the selected ball is from urn A? b) If a ball is randomly selected and found to be white, what is the probability that the c) If a ball is randomly selected from each urn, what is the probability that the selected two d) If two balls will be randomly selected from one of the urns without replacement, what is e) Suppose that we win S3 for each red ball selected, lose S1 for each black ball selected selected bal is from urn B? balls are different color? the probability that the selected two balls are in red color? and lose $2 for each white ball selected. If a ball is randomly selected from each urn, what is the probability that we will win the money?

Explanation / Answer

a)

probability of red=P(urn A and red +urn B and red) =(1/2)*(3/8)+(1/2)*(6/10) =39/80

therefore probability from Urn A given ball is red =P(urn A and red )/P(red) =(1/2)*(3/8)/(39/80)=15/39=5/13

b) as white ball is only in urn B ; therefore probability tht selected ball is from urn B =1

c)

probability that ball are different color =1-P(both are red) =1-(3/8)*(6/10)=62/80 =31/40

d)

probability that two balls are red =P(urn A and both red+urn B and both red) =(1/2)*(3/8)*(2/7)+(1/2)*(6/10)*(5/9)

=37/168

e)probability win money =1-P(black ball from urn A and white ball from urn B) =1-(5/8)*(4/10)=3/4

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