10% of the nylon bags produced by a machine are defective. Find the probability to have 4 defective bags at least out of 5 bags chosen randomly.

Question

Statistic

Answer 1

I think you may need to know the total number of bags, because once you choose 1 defective bag, the percentage of defective bags remaining in the group goes up. So if you have 100 bags, 10 will be defective, and your chance of choosing a defective bag on your first try is 10%; however, once you have chosen that, you now have 9 defective bags in a sample of 99, which is 9.1%. I hope that makes sense?

 

If you're replacing the bags though--that is, taking one out, evaluating whether it's defective or not, and putting it back, then the probability won't change each time and it's

 

0.1 x 0.1 x 0.1 x 0.1 x 0.9(since you're also choosing a functional bag--4 out of 5 are defective)

 

= 0.009% chance