Question
Two bad eggs are mixed accidentally with 10 good ones. Three eggs are drawn at random without replacement from this lot. Find the mean and variance for the number of bad eggs.
Solution
Let X represent the number of bad eggs. X takes the values 0, 1, 2.
P(X = 0) = P(3 good eggs)
P(X = 1) = P(2 good eggs and one bad egg)
P(X = 2) = P(one good egg and two bad eggs)
P(X = 0) = P(3 good eggs)
P(X = 1) = P(2 good eggs and one bad egg)
P(X = 2) = P(one good egg and two bad eggs)
