Probability


Probability is the measure of how likely an event will happen. Probability is usually expressed as a fraction or a decimal.

Probability of an event = P(event) =

Odds show how the chance of an event happening compares to the chance of the event not happening. Odds are usually expressed as a ratio.

Odds of an event =
Number of outcomes where the event happens : Number of outcomes where the event does not happen


Example 1: Rolling dice

A die (or one "dice") is rolled. What is the probability of rolling a 4?
When a die is rolled, you can get only 6 possible outcomes: 1, 2, 3, 4, 5, and 6.
Probability of rolling a 4 = P(rolling a 4) = =
A die is rolled. What are the odds of rolling a 4?
Odds of rolling a 4 =
Number of outcomes where you roll a 4 : Number of outcomes where you do not roll a 4

Odds of rolling a 4 = 1 : 5


Example 2: Highlighted pieces

Find the probability that a randomly selected piece of the shape will be highlighted and find the odds that a piece chosen will not be highlighted. Express probabilities as a simplified fraction and odds as a ratio of two numbers with no common factors other than 1 (i.e. "2:1").
Probability:
Odds:

P(selecting a highlighted piece) = = = =

Odds that a selected piece will not be highlighted =

Number of outcomes where a selected piece is not highlighted : Number of outcomes where a selected piece is highlighted
Number of unhighlighted pieces : Number of highlighted pieces
4 : 2
The odds 4:2 can be simplified to 2:1.

So the answer is Probability:
Odds:

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