Question

There are two small boxes $A$ and $B$. In $A$ there are $9$ white beads and $8$ black beads.
In $B$ there are $7$ white and $8$ black beads. We want to take a bead from a box.
(a) What is the probability of getting a white bead from each box?
(b) A white bead and a black bead are added to box $B$ an then a bead is taken from it.
What is probability of getting a white bead from it.

Answer 1

Total number of beads in box $A=9W+8B=17$
Total number of beads in box $B=7W+8B=15$
(a) P(getting a white bead from box A) = $\frac{9}{17}$
P(getting a white bead from box B) = $\frac{7}{15}$
(b) When a white bead and a black bead are added to box B,
Number of white beads in box $B=7W+1W=8W$
Number of black beads in box $B=8B+1B=9B$
Thus, total number of beads in box $B=8W+9B=17$
Hence, P(getting a white bead from box B) = $\frac{8}{17}$.