Binomial Experience

Question 1

Note: You have to show how you arrived at these values to get full points.

1. It is natural to model the gender of children that will be born from a family as a Binomial experiment. Let each childbirth be a Bernoulli trial, where “success” is defined as the child being a female. Let’s assume that these Bernoulli trials are independent, each with success probability p = 0.55. A family plans to have 4 children.

Let X be the number of females this family will have.
Let Y be the number of births until the family get a female child.

a. What is the distribution of X? (2pts)
b. What is the distribution of Y? (2pts)

Question 2

In order to solve this problem we must use the combination rule, which is nCr = n!/(n-r)!r!

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

Please write out answer in numbers and math terms step by step as well.