Probability: The long-term chance that a certain outcome will occur from some random process.
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0 0.25 or 1/4 0.5 or 2/4 0.75 or 3/4 1 or 4/4
0 resembles impossible whereas 1 resembles certain. Values in-between can vary from the likes of unlikely to likely. 0.4 or 2/4 resembles a half chance.
EXAM TIP: Write probability as a fraction and decimal in the exam!
In 1/2, it resembles one outcome and 2 possible outcomes.
4/5 resembles 4 outcomes and 5 possible outcomes.
In the event of Heads and Tails, Heads and Tails both have an equal chance (0.5 or 2/4) of happening, covering every possible outcome in two different outcomes. 0.5 x 2 = 1
In the event of Rock Paper Scissors, each has an equal chance of happening. This however does not mean they all have a probability of 0.5 or 2/4 since there are 3 values. For 3 values to have an equal chance they must all have a probability of 0.33... or 1/3. 0.33... x 3 = 1.
Experiment: A repeatable procedure with a set of possible results.
Sample Space: A possible range of result of an experiment.
Sample Point: One of the results within a sample space.
Event: Single or multiple outcomes of an experiment.
P (result or another result) = Addition.
P (result and another result = Multiplication.
In the event of rolling 2 dice, what are the chances of getting a 6 and a 6?
The chance of getting a six on one dice is 1.16... or 1/6, to get the chance of getting a six on the other dice is exactly the same, we multiply these probabilities.
1/6 x 1/6 = 1/36 because getting a 6 and a 6 is one outcome within 36 potential outcomes.
How about the chances of getting a number other then 6 and a number other then 6 on both dice rolls? The chance of getting 1, 2, 3, 4 or 5 in a dice roll is 0.83... or 5/6, this will be identical to the next roll too, we multiply these.
5/6 x 5/6 = 25/36 because getting anything but a six twice is 25 outcomes within the same 36 possible outcomes.
Using the results from the last scenario, you are able to determine that getting a 6 on either dice roll has a 11/36 chance of happening.
The two dice rolling experiment can also be presented as a tree diagram.
Through each branch, the chance of getting a 6 and not getting a 6 is presented. To find the probability of getting a 6 on either roll, you have to highlight what branch sequences contain at least one 6. Once then multiply each sequence and add the results.
(1/6 x 1/6) + (1/6 x 5/6) + (5/6 + 1/6) = 11/36.
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