Probability
Basics
We shall first explore the terminology and vocabulary
We use the probability to predict the chance of some something happening in the future. Below is a list of terms you’ll use when working with probabilities;
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Experiment: Is a repeatable process that gives rise to a number of outcomes.
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Event:Is a collection (or set) of one or more outcomes
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Sample space: Is the set of all possible outcomes of an experiment.
In statistics events are denoted by upper case letters. The probability of an event is the chance that the event will occur as a result of an experiment.
- An impossible event has probability 0 and an event that is certain has a probability 1
- When all outcomes in a sample space are equally likely the probability of any event is the number of all outcomes in the event divided by the total number of possible outcomes in the sample space
- All events have probabilities between impossible (0) and certain (1). Probabilities may be written as fractions or decimal or even percentages.
Examples
In this section we shall look at some simple examples of probabilities.
A fair die has numbered 1 to 6. The dice is thrown once and the number landing face up is recorded.
- Find the probability of the dice landing with the number 3 face up.
- Find the probability of throwing an odd number.
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The numbers that could land face up are; 1, 2, 3, 4, 5 or 6. So the sample space has six possible outcomes.
There are six faces and only one has 3 on it. Therefore the probability of landing with the number 3 is;
1/6 or 0.16There is only one outcome of landing a 3 out of all the six possible outcomes. So we divide 1 by all the six possible outcomes. - The event of ‘throwing an odd number’ has three outcomes. The 3 odd numbered faces are; 1, 3, and 5. Therefore the probability of throwing an odd number is;
3/6=1/2 = 0.5
Note we have divided the three outcomes by the total of six possible outcomes.
Two fair spinners each have four faces numbered 1 to 4. The two spinners are thrown together and the sum of the numbers indicated on each spinner is recorded.
- exactly 4
- more than 5
To solve this problem we shall draw two axes as shown below;
[IMAGE]
There are 16 points on the sample space. Each of the points is equally likely as the spinners are fair.
- In the diagram there are four 5 outcomes out of all the 16 outcomes, therefore;
P(4) = 4/16 = 1/4
- On the diagram there are 6 numbers more than 5, therefore;
P(More than 5) = 6/16 = 3/8
We can also write the number as a decimal of 0.375
- Venn diagrams probability
- Probability formulae
- Conditional probability
- Probability tree diagrams
- Mutually exclusive and independent events probability.
