Answer to Question #379 in Statistics and Probability for Elizabeth

Question

There are 90 good and 10 defective screws in the box. What is the probability that there are no defective screws among 10 randomly taken screws?

Answer 1

The total amount of screws in the box is: 90+10 = 100.
The number of ways to select 10 screws from 100 is: N = (C100)^10.
The number of ways to select 10 screws from good ones is: m = (C90)^10.
Thus, the probability of taking 10 good screws is: P = m/N = ((C90)^10)/((C100)^10) = (90!*90!)/(80!*100!) ≈ 0.33