One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. What will be the probability that the ball is white.
Tell me more
×
Mathematics Stack Exchange is a question and answer site for
people studying math at any level and professionals in related fields. It's 100% free, no registration required.
|
|
|
It would be the following: $$P(W) = P(W \cap W_1)+P(W \cap B_1)$$ $$ = P(W|W_1)P(W_1)+P(W|B_1)P(B_1)$$ $$= \frac{5}{9} \frac{8}{17}+ \frac{4}{9} \frac{7}{17}$$ where $W_1$ denotes the event that the first ball chosen is white, $B_1$ denotes the event that the first ball chosen is black, and $W$ denotes the event the the ball from the second bag is white. |
|||||
|
