I\'m stuck on this problem, not sure where to start. Could someone please help m

Question

I'm stuck on this problem, not sure where to start. Could someone please help me? Thank you!

Question:

In most industrialized countries the birthrate for boys is slightly higher than for girls. The chance of a mother giving birth to a boy is about 51.2%. Can you turn this statistic into a profitable--but likely illegal--business? Grab your crystal ball and head to the local maternity ward. You will charge pregnant women $10 to predict the gender of their child, and will, of course, always predict that the child will be a boy. If you are wrong, you can give the mother back her $10.

a) If you can get 1000 women to pay for your prediction, and return the money to all of the mothers having girls, how much profit will you expect to make? (Let’s just ignore the possibilities of multiple births.)

b) Now, how likely are the mothers with girls to actually track you down and demand their money back? Let’s say that 40% bother, what is your expected profit now?

Explanation / Answer

Given,

chance of giving birth to boy = 51.2%

profit if boy is born = 10$

profit if girl is born = 0$

a)

N = 1000

expected profit he would make

= 0.512 * 10 + ( 1- 0.512 ) * 0

= 5.12 $

b) If only 40% mothers with girls bother abt money

i.e ( 1- 0.512) * 0.6 donot bother abt money even if girl is born

= 0.2928

so, 0.7072 of population he gets profit, 0.2928 he gets nothing

expected profit

= 0.7072 * 10 + 0.2928 * 0

= 7.072$

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