Question

An urn contains 2 white balls and 8 red balls. A second urn contains 8 white balls and 2 red balls. An urn is selected, and the probability of selecting the first urn is 0.7. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)

(a) the probability that the urn selected was the first one


(b) the probability that the urn selected was the second one

Answer 1

P(2 white balls) =P(Urn 1)*P(2 white|urn 1)+P(Urn 2)*P(2 white|urn 2)

=0.7*(2/10)*(2/10)+0.3*(8/10)*(8/10)=0.22

a)

P(1st urn |2 white balls) =P(Urn 1)*P(2 white|urn 1)/P(2 white balls)=0.7*(2/10)*(2/10)/0.22=0.1273

b)

P(2nd urn |2 white balls) =P(Urn 2)*P(2 white|urn 2)/P(2 white balls)=0.3*(8/10)*(8/10)/0.22=0.8727