## Wednesday, January 30, 2013

### Can Chewing Gum Help Eleven Plus Understanding?

You and your child are discussing, once again, probability. There must be few ten year old children who worry about the chances of something happening – but if they are to write the eleven plus examinations successfully they will need to know something! We enjoyed the company of a very bright child the other day who was faced with working out the outcomes of heads or tails from two coins being thrown at the same time.

Our scholar grasped the concept almost before he had read the question. He then asked what would happen if one coin was tossed twelve times. One of our assistants is studying statistics and relished the chance of working on a rather abstract problem. Over the course of the lesson a table emerged.
 Number of Number of Heads tosses 12 1 11 12 10 66 9 220 8 495 7 792 6 924 5 792 4 495 3 220 2 66 1 12 0 1

It did not take long to work out that the most likely outcome of tossing a coin 12 times is to obtain 6 heads and 6 tails.

Obtaining 7 heads and 5 tails is less likely – but still probable.

It is very unlikely to obtain 12 heads in 12 tosses – and to obtain 12 tails in 12 tosses – but there still is a chance!

The eleven plus mathematics question emerged. “If the total number of outcomes of all the tosses is 4096, how do you work out the probability of obtaining 12 heads? Do you add, subtract, multiply or divide?”

A 1 divided by 4096