A box contains

Question

A box contains 1010 transistors, 44 of which are defective. If 44 are selected at random, find the probability that
a. All are defective.
b. None are defective

Answer 1

For all to be defective, the # ways to get this is 44C44, which is 1 (obviously--there's only one way to get them all).

The denominator 1010C44 is # ways to choose 44 transistors from the whole box.

 

The probability of all defective is 1/(1010C44).  Use your calculator!to compute this tiny result.  

 

The probability that NONE are defective is 1 minus the above (tiny) result.