Math help please!
There are three urns that each contain 10 balls. The first contains 3 white balls and 7 red balls, the second 6 white and 4 red, and the third all 10 white. Each urn has an equal probability of being selected. After an urn is selected a ball is randomly drawn from this urn. If the ball drawn was white, find the probability that the third urn was selected.
Three machines turn out all the products in a factory, with the first machine producing 25% of the products, the second machine 30%, and the third machine 45%. The first machine produces defective products 17% of the time, the second machine 18% of the time and the third machine 2% of the time. What is the probability that a non-defective product came from the second machine?
Urn A contains seven white balls and six black balls. Urn B contains three white balls and five black balls. A ball is first drawn from Urn A and then transferred to Urn B. A second ball is then drawn from Urn B. What is the probability that the first ball was white given that the second ball was white?