Question

A box contains 8 black beads and 12 white beads. Another box contains 9 black beads and 6 white beads. One bead from each box is taken.
a) What is the probability that both beads are black?
b) What is the probability of getting one black bead and one white bead?

Answer 1

First box contains 8 black and 12 white beads Second box contains 9 black and 6 white beads.
(a) One black bead from each box is taken.
Number of such cases = $8\times 9=72$
Total number of possibilities = $20\times 15=300$
Probablity of getting both black beads = $\frac{72}{300}=\frac{6}{25}$
(b) One black and one white bead is taken.
So if one black bead is taken from first box then one white bead is taken from second box and if one white bead is taken from first box then one black bead is taken from second box.
Number of such cases = $8\times 6+12\times 9=48+108=156$
Total number of possibilities = $20\times 15=300$
Probablity of getting one black and one white bead $=\frac{156}{300}=\frac{13}{25}$