20.18 An expected rip-off? A “psychic” runs the following ad in a magazine:
Expecting a baby? Renowned psychic will tell you the sex of the unborn child from any photograph of the mother. Cost, $20. Money-back guarantee.
This may be a profitable con game. Suppose that the psychic simply replies “boy” to all inquiries. In the worst case, everyone who has a girl will ask for her money back. Find the expected value of the psychic’s profit by filling in the table below.
Sex of child |
Probability | The psychic’s profit |
Boy | 0.51 | |
Girl | 0.49 |