Sum

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?

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#### Solution

Number of fuses = 5 + 2 = 7

Testing two fuses one-by-one at random, without replacement from 7 can be done in ^{7}C_{1} × ^{6}C_{1} ways.

∴ n(S) = ^{7}C_{1} × ^{6}C_{1} = 7 × 6 = 42

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

There are two defective fuses.

∴ n(A) = ^{2}C_{1} × ^{1}C_{1} = 2 × 1 = 2

∴ P(A) = `("n"("A"))/("n"("S"))`

= `2/42`

= `1/21`

Concept: Concept of Probability

Is there an error in this question or solution?

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