Question

U have 10 batteries sitting on your desk, three of which are dead. You choose 2 batteries are random for you calculator. What is the expected number of good batteries that you get?
0
1
1.4
2

Answer 1

You have to calculate the expected value of pulling any number of good batteries.
There are 3 bad batteries (B) and seven good batteries (G)
If you pull two batteries the possible number of good batteries you can get are 0, 1 and 2.
GB, BG, GG, and BB
two chances for getting 1, one chance for getting two, and one chance for getting zero.
In order to calculate the expected value you have to first calculate the values of all the possibilities.
(GB = 7/10 x 3/10) (BG = 3/10 x 7/10) (GG = 7/10 x 7/10) (BB = 3/10 x 3/10)
Then take these answers and multiply them by the number of good batteries they each contain and add. (GB is 1 good battery, GG is two, etc.)
1(.21) + 1(.21) + 2(.49) + 0(.09)
The result is 1.4
The expected value of good batteries is 1.4