Marie claims she can predict the sex of pregnant womens babi

Marie claims she can predict the sex of pregnant women\'s babies. She sees 1,000 women a year, and she always predicts a female. She charges $1,000 for a prediction, and she always predicts a female (although clients do not know that). When she is wrong, she offers a double-your-money back guarantee. Since the chance of having a female is approximately 50%, how can she earn any money?

Solution

The payoff for marie will be:

Payoff ( X = male) = - 1000

Payoff (X = female) = +1000

If the chances of being correct are EXACTLY 50%, then she would operate on a no-profit and no loss basis

However, to earn any money,

p(X=female) = (0.50 + e)

p(X=male) = (0.50 - e)

Thus, net payoff = 1000*(0.50 + e) + (-1000)*(0.50 - e)

= 2000e

Thus, Marie can earn any money if and only if e > 0

Hope this helps. Ask if you have any doubts.