An urn contains 4 white balls and 10 blue balls and a second urn contains 14 white balls and 5 blue balls. 1 ball is drawn from the first urn and placed in the second urn. What is the probability that a ball now drawn in the second urn is white?
An urn contains 4 white balls and 10 blue balls and a second urn contains 14 white balls and 5 blue balls. 1 ball is drawn from the first urn and placed in the second urn. What is the probability that a ball now drawn in the second urn is white?
P(white) = P(ball from first urn was white)P(white ball in second urn after transfer of white ball) + P(ball from first urn was blue)P(white ball in second urn after transfer of blue ball)
This takes in account all situations.
$\displaystyle P(W) = \frac{4}{14}*\frac{15}{20} + \frac{10}{14}*\frac{14}{20}$