# What is Probability?

Probability is a measurement that is applied to events. It is the measurement of the likelihood, or chance of an event happening.

## Introducing Probability

Discuss and explore doubt and certainty with your children. Use the "language of probability" when discussing whether you think events will or will not happen. For example:

• certain
• definitely
• very likely
• equally likely
• roughly even
• very unlikely
• definitely not
• impossible

A good way to introduce probability is to choose and discuss a number of different events and rank them in order based on how likely you think it is that they will occur. Such discussions will often be subjective and different people will rank events in a different order based on their own experiences and opinion. Ordering events this way just requires a judgment on whether an event is more, or less, likely to happen than the other chosen events.

## Scale For Measuring Probability

The next stage after ranking events in order of likelihood is to use language of as a form of measurement. Terms such as those listed above (e.g. "certain", "very likely", "impossible") can be attached the events. This can be followed by the introduction of numeric values as a measure of probability. As the table above shows, a scale of 0 to 1 can be used to measure possibility.

• 0 equates to an impossibility,
• 1 equates to a certainty, and
• 0.5 equates to an even chance.

## Measuring Probability

Having used the language of probability to subjectively describe the chances of various events happening, we can move on to use more objective methods that are based more on evidence than on opinion. Two such methods are described below.

### Theoretically

Probability can be calculated using the formula below:

 Theoretical Probability = Total Favorable Outcomes Total Number of Possible Outcomes

The two examples below show how the formula can be applied using the example of a deck of 52 playing cards that have been shuffled and that are in no particular order.

What is the probability of turning over the six of diamonds?
There is only 1 six of diamonds in a pack of 52 cards.
 P (6 of diamonds) = 1 52
What is the probability of turning over a King?

There are only 4 Kings in a pack of 52 cards.

 P (King) = 4 52
Probability can be shown as a fraction, a percentage, or a decimal.

The probabilities above can be shown as follows:

Fraction Simplified
Fraction
Percent Decimal
P (6 Diamonds)
 1 52
 1 52
1.9% 0.019
P (King)
 4 52
 1 13
7.7% 0.077

Note: "P" followed by the event referred to in parenthesis is used to represent probability in formulas.

If needed, you will find help here on simplifying fractions and there is also more on converting from fractions to decimals here.

### By Experiment

The two "classic" experiments that you can do with your children are the coin toss and the roll of the dice. Before doing these, discuss what the expected outcomes might be. e.g. "how many times do you expect tails to come up if we toss the coin 50 times?" Record the outcomes and use the formula below to compare the results to the theoretical probability.

 Experimental Probability = Number of occurrences Total number of attempts

Repeat the experiment with different numbers of attempts. Discuss with your children how the results might compare if if just a small, or a very large number of attempts are made.

## Independent Events

If you have two dice you can use them with your children to explore and experiment with probabilities for two independent events. Predicting the number of possible outcomes with more than one event can be tricky. Using a table, like the one below, showing all possible outcomes for each event is a good help.

The table below shows all possible outcomes when rolling two dice, A and B.

 A B 1 2 3 4 5 6 1 1,1 2,1 3,1 4,1 5,1 6,1 2 1,2 2,2 3,2 4,2 5,2 6,2 3 1,3 2,3 3,3 4,3 5,3 6,3 4 1,4 2,4 3,4 4,4 5,4 6,4 5 1,5 2,5 3,5 4,5 5,5 6,5 6 1,6 2,6 3,6 4,6 5,6 6,6

What is the probability of rolling a total of 5?

We need to identify the number of outcomes that result in a total of 5. Looking at the table we can see there are 4 such outcomes.

We then divide by the total number of possible outcomes which is 36.

 P (Total of 5) = 4 = 1 36 9

## Probability Worksheets

The worksheets below provide practice with calculating probabilities.