Stat

Bag A has 10 black balls and 1 white ball. Bag B has 12 black balls and 1 white ball. Jane has Bag A and Dick has Bag B. They draw with replacement from their bags at the same time (independently) until someone draws a white ball. (Then the person who did not draw a white ball does the dishes.) Find the probability that...

a. they draw the first white ball at the same time (after equal number of attempts). Round your answer to 4 decimal places.

b. Dick draws the first white ball before Jane does. Round your answer to 4 decimal places.