Question

Find the probability that at least 2 are defective bulbs out of 4 bulbs drawn from a box containing 10 bulbs. Out of the 10 bulbs, we know that 3

Answer 1

There are 3 ways of choosing the 2 bulbs.

Both the chosen bulbs are non defective, and probability of that is 18C2 / 20C2 = 153/190 as you have already calculated.

Both the bulbs are defective, and probability for that would be 2C2 / 20C2 = 1/190.

One bulb is defective and other one is not, and probability for that would be 18C1 x 2C1 / 20C2 = 36/190.

Now, probability of choosing both non-defective bulb would be

=1- P(condition2) - P(condition3)

=1-1/190-36/190

=153/190