Chance can be expressed either as a probability or as odds. In most contexts, there is no particular reason to prefer one to the other. Most scientists tend to feel more comfortable thinking about probabilities whereas sports enthusiasts tend to talk about odds. These are matters of training and custom, not standards.
Odds are always expressed as ratios. Probability is expressed as a real number between zero and one. Zero represents no chance of the event happening and one represents that the event will happen with certainty.
Consider a fair coin. It has an equal chance of getting heads or tails. When flipping the coin, you might guess instinctively that the probability of it coming up
heads
is 50%. That is correct. Because only two outcomes are possible, each outcome has a 50% chance of occurring. This means you have a
probability of getting the outcome
heads
. Now, express this as odds. Odds is the ratio of events that will occur,
heads
, to events that will not occur,
tails
. The odds are 1:1 which is commonly called
even money
.
In the study of odds and probability, events that will occur are often referred to as favourable outcomes and events that will not occur are referred to as unfavourable outcomes .
Consider another example. Roll a fair six-sided die. If you wanted to roll a two, you have a one in six chance because only one side of six has a two on it. In other words, the probability of rolling a two is
. Expressed as odds the ratio of favourable outcomes, rolling a two, to unfavourable outcomes, not rolling a two, is 1:5.
|
Watch the
Calculating Odds and Probability
video to see another example comparing odds and probability.
|
|
Read page 143 Example 1 in your textbook, Principles of Mathematics 12 . Complete the Your Turn questions on page 143 (a & b) for more practice in determining odds. Click here to verify your answers . |
Often converting between probability and odds is useful. Examples 1 and 2 explore this.