Approximately 3 percent of all children born in a certain region are from multiple births (that is, twins, triplets, etc.). Of the children born in the region who are from multiple births, 20 percent are left-handed. Of the children born in the region who are from single births, 10 percent are left-handed.

(a) What is the probability that a randomly selected child born in the region is left-handed?

(b) What is the probability that a randomly selected child born in the region is a child from a multiple birth, given that the child selected is left-handed?

(c) A random sample of 20 children born in the region will be selected. What is the probability that the sample will have at least 3 children who are left-handed?

(d) In the previous question, what is the expectation and variance of the number of left-handed children in the sample?