Answer to Question #180583 in Statistics and Probability for zach

Question

.One bag contains 4 white balls and 2 black balls, another contains 3 white balls and 5 black balls. If one ball is drawn from each bag. Find the probability that;

a)     Both are white

b)     Both are black

c)      One is white and one is black

Answer 1

There are 6 balls in total in the first bag and 8 in the second one.

a) $\displaystyle P(A) =\frac{4}{6} \cdot \frac{3}{8} = \frac{1}{4}$

b) $\displaystyle P(B) = \frac{2}{6} \cdot \frac{5}{8} = \frac{5}{24}$

(c) $\displaystyle P(C) = P(wb) + P(bw) = \frac{4}{6} \cdot \frac{5}{8} + \frac{2}{6} \cdot \frac{3}{8} = \frac{5}{12} + \frac{1}{8} = \frac{13}{24}$