1. Lesson 3

1.2. Explore

Mathematics 30-3 Module 1

Module 1: Probability

 

Explore

 

odds: a ratio that compares a desired event to the number of undesired events or vice versa

 

Source: MathWorks 12 Student Book/Teacher Guide. (Vancouver: Pacific Educational Press, 2011.)

In Try This 1 and Share 1, you should have noticed that the number of red shapes added to the number of non-red shapes equals the total number of shapes. You could express this ratio in the following ways:

  • the number of red shapes:non-red shapes
  • the number of red shapessadtotal number of shapes − number of red shapes)

You also should have noticed that the probability of choosing a red shape added to the probability of choosing a non-red shape is 1.

 

So far in this module you have used probabilities to compare the likelihood of events, such as rain on your camping trip, occurring. Another method of comparison is to use odds. You might want to compare the odds of getting into a technical school to the odds of getting an apprenticeship when you finish school.

 

tip

Since odds are a ratio, they can be simplified in the same way as fractions.

 

Simplifying a Fraction

Simplifying Odds

6:18 = 1:3

For example, the odds of rolling a four on a standard six-sided die are 1:5, read as “one to five” since there is 1 four and 5 non-four sides. Notice that there are a total of six sides, one with a four and five with numbers other than a four.

 

You can also list the odds against an event. In this situation, the ratio compares the unfavourable events to the favourable event, which is the one you want to occur. The odds against rolling a four are 5:1, read as “five to one.”

 

The left side of the diagram shows a die with the four side showing and is labelled “1 favourable outcome.” The right side of the diagram shows 5 dice with one, two, three, five, and six showing, and is labelled “5 unfavourable outcomes.”

 

In Try This 2 you will use your knowledge of the number of favourable events compared to the number of unfavourable events and their relationship to the total number of events.

 

Try This 2

 

This is a photo of a girl with a badminton racquet.

Ingram Publishing/Thinkstock

Estella is a member of her school’s badminton team. She joins 4 other players from her school to compete in a singles tournament with 65 players from other schools.

 

Assuming that all players are evenly matched, answer the following questions.

  1. Determine the odds for Estella winning the tournament.
  2. Determine the odds against Estella winning the tournament.
  3. Determine the odds against a student from Estella’s school winning the tournament.
  4. Determine the odds for a student from Estella’s school, who is not Estella, winning the tournament.

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Share 2

 

With a partner or in a group, share your responses to the questions in Try This 2.

 

Suppose Estella and the other 4 players from her school have a practice tournament. In the past, Estella has won most of the practice tournaments. Are her odds of winning this practice tournament 1:4? Explain.

 

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