Question

A box contains 4 black beads, 6 white beads, and 10 red beads. Another box contains 7 black beads, 5 white beads, and 8 red beads. If we take one bead from each box, without looking into it, what is the probability of getting at least one black bead?

Answer 1

Number of beads in each box = 20

Total number of ways of selecting two beads = 20× 20 = 400

Number of beads having atleast one black bead

= 4 × 7 + 4 × 5 + 4 × 8 + 6 × 7 + 10 × 7

= 28 + 20 + 32 + 42 + 70

= 192

Probability of having at least one black bead = \(\frac{192}{400} = \frac{12}{25}\)