If a box contains 75 good IC chips and 25 defective chips, and 12 chips are selected at random Find
i) the probability that no chip is defective.
ii) the probability that atleast one chip is defective
You have 100 chips. 75 are good. 25 are bad.
Select 12.
First one:
75/100 chance of not being defective.
Second one:
74/99 chance of not being defective (because you've removed one of the good chips)
Third one:
73/98...
So the probability of the first three chips being good is
$\displaystyle \frac{75}{100} * \frac{74}{99} * \frac{73}{98} = ...$
Proceed in the same vein for 12 chips...
ii) Probability that at least one chip is defective...
Well, the complement of this is that NO chips are defective. Which, conveniently, is the probability that we have just calculated.
So, total probability = 1, as always. Probability of complement = (previous answer).
Then we want:
1 - (previous answer) = probability of our outcome / (at least one chip is defective )