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
B 1 added to 4096
C 1 taken from 4096
D 1 multiplied by
4096
You then hope that your child comes up with the right answer
and then remarks: “If the coin did come up heads ten or eleven or twelve times
it is likely that someone is cheating! I bet someone stuck chewing gum on one
side.” If this is the response you know all your hard work is paying off! Your
child has a good understanding of at least one aspect of probability.
