Boy or girl?
Will the witch make a profit or loss?
Age
14 to 16
Challenge level
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.