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 90C5 ways.
There are a total no. of 100C5 ways.
So required probability =90C5/100C5=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?