A box of light bulbs has 6 75W bulbs, 4 40W bulbs, and 5 60W bulbs. If 2 bulbs are taken from the box and one is a 75W bulb, what is the probability that both are 75W? If neither bulb is 75W what is the probability that both have the same wattage?
1 Answer
Oct 9, 2015
This is a typical example of the urn-model. You may as well take them one by one.
Explanation:
(1)
Say the first is a 75. Then there are 5 75's left on a total of 14.
(2)
The first is not a 75, so either a 60 or a 40:
(a) first is a 60 (chance 5/15).
Then there are 4 60's left on a total of 14
Multiply because of first AND second being 60:
(b) first is a 40 (chance 4/15).
Then there are 3 40's left on a total of 14
Multiply because of first AND second being 40:
Now add these two, because it's EITHER 2 60's OR two 40's: