# Boy or Girl?

Will the witch make a profit or loss?

## Problem

A witch claims that she can predict whether your baby will be a boy or girl, and she charges £100 for this service.

If her prediction is wrong, she offers to return your £100 fee and pay you an extra £50 compensation for any distress that she may have caused.

Assuming she does not have any supernatural powers, can you explain whether she is likely to make a profit or loss after 100 clients have given birth?

*If you liked this problem, you might also like the article it appears in, Con Tricks*

## Student Solutions

If the witch is guessing, then in the long term, half of the time she will get it right.

So half of the time, she will keep £100, and half of the time, she will have to give the £100 back

**and**pay £50 compensation.

So half of the time, she will make £100. The other half of the time she will lose £50.

This means that after 100 babies have been born, she can expect to have gained £5000 and paid out £2500, so she will be £2500 in profit.