probability

Question

If from each box of the three boxes containing $3$ white and $3$ black,$2$ white and $2$ black,$1$ white and $3$ black,one ball is drawn at random ,then the probability that $2$ white and $1$ black ball will be drawn ?

Answer 1

2 white and 1 black balls can be obtained in following scenarios:

White from first, White from second and Black from third OR White from first, Black from second and white from third OR Black from first, White from second and White from third:

$Prob(\text{2 Whites and 1 Black ball}) = \frac{3}{6}*\frac{2}{4}*\frac{3}{4} + \frac{3}{6}*\frac{2}{4}*\frac{1}{4} + \frac{3}{6}*\frac{2}{4}*\frac{1}{4}$

$ = \frac{5}{16}$

Comments

from where that 2/4 is coming?

---

In the second box, there are 2 black and 2 white ball. Hence, probability for selecting a white ball is 2/4 and same for selecting a black ball.