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## Homework Statement

In a box containing 100 bulbs, 10 are defective. The probability that out of a

sample of 5 bulbs, none is defective is?

## The Attempt at a Solution

I see two approaches to this problem.

1) Out of 90 non-defective bulbs, we can chose 5 in

^{90}C

_{5}ways.

There are a total no. of

^{100}C

_{5}ways.

So required probability =

^{90}C

_{5}/

^{100}C

_{5}=0.5838

2) Out of the sample of 5 bulbs,

Probability of a non-defective bulb = 90/100=9/10

In 5 bulbs, required probability = (9/10)

^{5}=0.59049

The two answers don't differ by much. Which one is correct and why?