Answer to Question #4667 in Statistics and Probability for Elizabeth

Question

In a shipment of 50 transformers, 6 are known to be defective. If 30 transformers are picked at random, what is the probability that all 30 are nondefective? Assume that all transformers look alike and have an equal probability of being chosen.
Round your answer to 6 decimal places.

Answer 1

We can choose 30 transformers from 50 in 50!/(30!20!) & different ways.
As we
want all 30 to be non-defective (30 from 44), the number of proper variants is
44!/(30!14!).
According to the classical definition of probability,
we get
P = (44!/(30!14!)) / (50!/(30!20!)) = 44!*20!/(50!*14!) = 0.002439.