Question

A room has 3 sockets for lamps. From a collection of 10 light bulbs of which 6 are defective, a person selects 3 bulbs at random and puts them in a socket. What is the probability that the room is not lighted

Answer 1

The probability of placing a bad bulb on the first socket is 6/10. Then, for the second and third are 5/9 and 4/8 respectively. Therefore, the probability of ending with a dark room is (6/10)(5/9)(4/8) = 6!7!/10!3! = 1/6 = 0.1667 Finally, we subtract that from 1 to know the probability of having light in the room is 5/6 or 83.3%