A piece of electronic equipment contains six transistors Thi

A piece of electronic equipment contains six transistors. This piece of equipment is to be tested: the testing regime involves selecting two transistors at random and checking to see if they are defective. The equipment only passes the test if neither of the randomly selected transistors are defective. If the piece of equipment has two defective transistors, what is the probability that it will pass the test?

Solution

First, note that this is selection WITHOUT replacement, so it is NOT Binomial but is Hypergeometric.

given that six transistors with 2 bad and 4 good ...
total possible cases for Selecting 2 transistors from 8 (n) =8C2

Now favourable cases(m) =4C2

Now the probability that it will pass= m / n

P=4C2/ 8C2 = 6/28 = 3/14 = 0.214

P=21.4%