Question

By accident, 4 burned out bulbs have been mixed in with 20 good ones. ken is replacing old bulbs in his house. if he selects two bulbs at random from the box of 24, what is the probability they both work?

Answer 1

`\displaystyle |\Omega|=\binom{24}{2}=(24!)/(2!22!)=(23\cdot24)/(2)=276\\ |A|=\binom{20}{2}=(20!)/(2!18!)=(19\cdot20)/(2)=190\\\\ P(A)=(190)/(276)=(95)/(138)\approx69\%`

Answer 2

the probablility that the first one works is 20/24 = 5/6
next, there are 23 left, including 19 good ones. So the probability is 19/23.
Multiply 19/23 and 5/6 to get 95/138, which is out answer.