Statistics-I need help please

Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defective unit. The Condor Electronics Company has just manufactured 4000 gamedisks, and 170 are defective. If 5 of these gamedisks are randomly selected and tested, what is the probability that the entire batch will be rejected?

Report the answer as a percent with one decimal place accuracy. (You need not enter the "%" symbol)

Probability = 

Answer 1

Exact solution:

P(at least one of 5 defective) = 1 - P(none of 5 defective)

Use combinations to calculate the probabilities.

Total ways to select 5 out of 4000: ₄₀₀₀C₅

Ways to select 5 out of 4000 -170 = 3830 not defective: ₃₈₃₀C₅

P(none of 5 defective) = favorable outcomes / total outcomes = ₃₈₃₀C₅ / ₄₀₀₀C₅ = 0.805

P(at least one of 5 defective) = 1 - 0.805 = 0.195 = 19.5%

Approximate solution:

You can use Binomial distribution because when you take out a unit for testing, its probability to be defective stays approximately constant due to the large population of size 4000 and the large group of defective units of size 170.

So use Binomial probability:

n = 5 trials

p = 170/4000 probability for a unit to be defective

P(X ≥ 1) = 0.195 with any Binomial calculator, giving the same answer to the third digit as before.