# Chance (Possible Result)

## Chance (Possible Result)

Possibility that an event will occur or the possibility of obtaining a particular result in a random experiment.

$$\dfrac{\text{number of favourable results}}{\text{number of unfavourable results}}$$

$$\dfrac{\text{number of unfavourable results}}{\text{number of favourable results}}$$

### 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 $$\dfrac{1}{5}$$ or 1 : 5 while the “chances against” are $$\dfrac{5}{1}$$ 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.”

This concept belongs to the general idea of opportunity, risk, possibility, or luck. To facilitate an introduction to probability, it’s preferable to use the term “possibility”. That way, we can say that there is one possibility out of 6 for rolling a 6 on an honest die.