Mathematics in Education and Industry

Mathematics in Education and Industry was founded in the early 1960s and is an independent UK curriculum development body.

MEI is committed to improving Mathematics Education and is involved in a range of activities to fulfil this aim:

• National discussions
• School syllabuses
• Resources
• CPD
• Special programmes

The majority of MEI's members are classroom mathematics teachers in schools and colleges.

MEI is a registered charity.

Maths item of the month

Finding the highest card

On 30 cards I write 30 different numbers, shuffle them thoroughly and place them face down in a pile on a table. You have no idea how big any of my numbers are. You turn over one card at a time, look at the number and decide whether you want to stick with that card or discard it and turn over the next card. Once a card has been discarded you cannot go back to it. What strategy should you use in order to maximise your chances of selecting the card containing the biggest number?

A possible strategy:
Do not keep any of the first 10 cards you turn over but remember the biggest number and call this number N. From the 11th card on, as soon as you see a number bigger than N, stop there. Of course, you might not see another number bigger than N in which case you will end up turning over all the cards without ‘winning’.

With this strategy, what is the probability that you will select the biggest number?

More maths items of the month