Problem #PRU-65355

Problem

The probability of the birth of twins in Cambria is \(p\), and no triplets are born in Cambria.

a) Evaluate the probability that a random Cambrian that one meets on the street is one of a pair of twins?

b) There are three children in a random Cambrian family. What is the probability that among them there is a pair of twins?

c) In Cambrian schools, twins must be enrolled in the same class. In total, there are \(N\) first-graders in Cambria.

What is the expectation of the number of pairs of twins among them?