In most industrialized countries, the birthrate for boys is slightly higher than

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? (ignore 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

Solution:-

The probability of a mother giving birth to a boy = 51.2/100 = 0.512

The probability of a mother giving birth to a girl = 0.488

a) Expected profit = $ 5120.

Expected profit = 1,000 × (Expected profit on one prediction)

Expected profit = 1,000 × {10 × 0.512 + 0 × 0.488}

Expected profit = $5120

b)

Expected profit = $ 8,048

Expected profit = 1,000 × (Expected profit on one prediction)

Probability that mothers with girls to actually do not track you down = 1 - 0.40 = 0.60

Expected profit = 1,000 × {10 × 0.512 + 10 × (0.60 × 0.488) )}

Expected profit = $ 8,048

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