If 6 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 1950 write-rewrite CDs, and 80 are defective. If 6 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Rounded to four decimal place accuracy.

Answer 1

(1950-80)1950 x (1949-79)/1949 x(1948-78)/1948 x (1947-77)/1947 x (1946-76)/1946x (1945-75)/1945

= 1870/1950 x 1870/1949 x 1870/1948 x 1870 /1947 x 1870/1946 x 1870/1945

= 1870^6/1950x1949x1948x1947x1946x1945

=.783765

= 78.3765%