In 1995 a study was done of all 10-year old amateur hockey players in Ontario. At the time, there were 22 000 children in this group. Of all those surveyed, only 11 later played in the National Hockey League (NHL). Given these statistics, determine each of the following.

  1. odds for making the NHL
  2. odds against making the NHL
  3. probability of making the NHL
  4. probability of not making the NHL

Number of possible outcomes = 22 000

Number making the NHL = 11

Number not making the NHL = 22 000 - 11 = 21 989

  1. The favourable outcome is making the NHL.

odds in favour = favourable outcomes : unfavourable outcomes = 11 : 21 989

The odds of making the NHL are 11 to 21 989.

  1. To find the odds against just reverse the positions of your odds in favour response.

The odds of not making the NHL are 21 989 to 11.


In Example 3d, you might have noticed a new notation, P ( A '). This denotes the complement of an event. In Example 3, the event is making the NHL , so the complement is not making the NHL . The complement can be thought of as a not probability, the chance of an event not happening . If you consider an event and its complement, you know that one or the other must happen. This means that, if you add the probabilities of either happening, you should get 1 or 100%.