Early accounts of Australia told stories of men gambling
with `Two Up’.  Two coins were tossed
into the air and there were bets on the results. Some of the bets were small –
but others were life changing.
If there were two heads the thrower won. With two tails the
thrower lost. If there was a head and a tail then the throw was made again.
No self -respecting eleven plus parents would ever want to gamble
with their child – but it could be an interesting way of a child learning about
the laws of chance and probability. (Is playing for matches gambling?)
Questions on probability could, possibly, come up in the eleven
plus. Consider a question along these lines:
You look at the boys and girls in your class of 25. Some are
wearing glasses. You are asked to make an analysis.
| 
   | 
  
   
Boys 
 | 
  
   
Girls 
 | 
 
| 
   
Glasses 
 | 
  
   
4 
 | 
  
   
5 
 | 
 
| 
   
No Glasses 
 | 
  
   
5 
 | 
  
   
11 
 | 
 
The person sitting beside you is a girl. She wears glasses.
Nine people wear glasses so the probability of her wearing
glasses is 9 out 25.
Only 4 boys wear glasses. This suggests 4 out of 9.
What is the probability of a girl wearing glasses?
What is the probability that the girl sitting beside you
will be wearing glasses?
You could also explore probability using a table.
Probability is measured on a scale – where zero represents
impossibility and one represents certainty.
| 
   
Passing the eleven plus while asleep 
 | 
  
   | 
  
   | 
  
   | 
  
   | 
  
   | 
  
   | 
  
   | 
  
   
Being either a boy or a girl 
 | 
 
| 
   
0 
 | 
  
   | 
  
   
0.25 
 | 
  
   | 
  
   
0.5 
 | 
  
   | 
  
   
0.25 
 | 
  
   | 
  
   
1 
 | 
 
| 
   | 
  
   | 
  
   | 
  
   | 
  
   
One coin landing either heads or tails 
 | 
  
   | 
  
   | 
  
   | 
  
   |