Chance (Possible Result)
Possibility that an event will occur or the possibility of obtaining a particular result in a random experiment.
- "chances for" In an experiment where the universe of possible outcomes is made up of equally probable results (random experiment), we determine the "chances for" an event using the ratio:
[latex]\dfrac{\text{number of favourable results}}{\text{number of unfavourable results}}[/latex]
- "chances against" In an experiment where the universe of possible outcomes is made up of equally probable results (random experiment), we determine the "chances against" using the ratio:
[latex]\dfrac{\text{number of unfavourable results}}{\text{number of favourable results}}[/latex]
Example
Consider the random experiment that consists of rolling an honest die with six faces numbered 1 to 6 and noting the result obtained. The universe of results is Ω = {1, 2, 3, 4, 5, 6}. The "chances for" obtaining a 6 are [latex]\dfrac{1}{5}[/latex] or 1 : 5 while the "chances against" are [latex]\dfrac{5}{1}[/latex] or 5 : 1.Educational Note
The idea of "chance" is familiar to students in all grades. This word is used in many common expressions, such as:- "I've got one chance to do this."
- "I solved this problem by chance."
- "If I leave at 1 p.m., I have a better chance of making it to my appointment on time."
- "When rolling a regular die with 6 faces numbered 1 to 6, I have one chance out of 6 of getting a 4."
- "I never had a chance."