Question

Solve the following:

Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-byone, at random and without replacement. What is the probability that we are lucky and fine both of the defective fuses in the first two tests?

Answer 1

Number of fuses = 5 + 2 = 7

Testing two fuses one-by-one at random, without replacement from 7 can be done in ⁷C₁ × ⁶C₁ ways.

∴ n(S) = ⁷C₁ × ⁶C₁ = 7 × 6 = 42

Let event A: Getting defective fuses in the first two tests without replacement.

There are two defective fuses.

∴ n(A) = ²C₁ × ¹C₁ = 2 × 1 = 2

∴ P(A) = `("n"("A"))/("n"("S"))`

= `2/42`

= `1/21`