Probability is used to express a specific and predictive value (in the form of a percentage or fraction) while odds compare the degree of confidence about a future outcome (in the form of a ratio). It is the chances in favour of an event occurring versus the chances against the same event from occurring. The odds against an event is the reverse ratio. Keep in mind that odds are NOT the same as probabilities.








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ODDS IN FAVOUR of an event occurring:

The probability of selecting the purple box is ¼ or 1 box out of a total of 4 boxes.
The odds in favour of the purple box is 1:3 or 1 purple box against 3 white boxes


or


Note:


Odds in favour are written as P(A) : P(A')



Example 1: Determining The Odds.
David came across a box of cell phones. The box contained four blue phones, seven red phones, and two pink phones. What are the odds in favour of David picking a pink cell phone out of the box?

Event A will be picking a pink phone out of the box. The probability of event A is:


The probability of not picking a pink phone from the box is:


Recall that the odds in favour or A can be written as P(A) : P(A'), therefore the odds in favour of event A are:


Therefore, the odds in favour of David picking a pink cell phone out of the box are 2:11.

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ODDS NOT IN FAVOUR of an event occurring:



Odds not in favour are written as P( A') : P(A)

As you notice, this formula is the reciprocal (complementary) of the formula used for finding odds in favour of an event occurring.

Example 2: Odds Against An Event.

The probability of a certain student being late in one week for Mr. D'Onofrio's fourth period Data Management class is 0.6. This data is based on the number of detentions the student has had so far. What are the odds that the student will arrive on time detention free this week?

The probability of the student arriving on time for Mr. D'Onofrio's class:



Therefore it is a 2:3 chance that the student will arrive on time detention free this week


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Example 3: Odds in favour of A are .

The odds of Jack getting accepted to the University of Toronto is 3:8. What is the probability of Rico not getting accepted to the University of Toronto?


Therefore, the probability of Jack not getting accepted to the University of Toronto is .

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Remember that odds give the degree of confidence that an event will or will not occur. So that means that the higher the ratio, then the higher the degree of confidence that event will or will not occur.

Example 4: Ratios.

If someone was to tell you that the odds of the Toronto Raptors making the playoffs is 5:1 then you are more confident than if they were to tell you the odds of the Toronto Raptors making the playoffs is 4:1.
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Example 5: P( A') =

What are the odds in favour of A happening?


Therefore, the odds in favour of A happening is 1:3.
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