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?

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Solution

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

Probabality of having at least one black bead = $\frac{192}{400}$ = $\frac{12}{25}$

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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?

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 Probabality of having at least one black bead = 192400=1225