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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?
Solution
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`
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