# 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 probab - Mathematics and Statistics

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?

#### 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

Concept: Concept of Probability
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (15) | Page 214