In families with four children what proportion of the famili

In families with four children, what proportion of the families will have at least one boy? In families with two girls and one boy, what fraction of the families will have the boy as the second child? In families with four children, what fraction of the families will have the gender order male-female-female-male?

Solution

In families with four children, proportion of the families will have at least one boy = 1 - having no boy

                                                                                                                                = 1 - 1/2 * 1/2 *1/2 * 1/2 = 0.9375

In families with two girls and one boy, fraction of the families will have the boy as the second child = 2C1 * 1/2 * 1/2 * 1/2 = 0.25

In families with four children, fraction of the families will have the gender order male-female-female-male = 2C1 * 1/2 * 2C1 * 1/2 * 1/2 * 1/2 = 0.25