Probability

Probability all is all about the chance of something happening.

Probability Words
If a question asks you to describe the probability using words the words most often used are

Impossible - Absolutely no chance it will happen
Unlikely - there is a small chance it will happen
Even Chance - the probability is a half or 50 - 50
Likely - it is not definitely going to happen but there is a good chance
Certain - it will definitely happen.

These words can be displayed, with numbers along the probability scale.



The Probability Scale

Probability Calculations

Probability of something happening
If the question asks you to calculate the probability the answer will need to be given as a numerical answer usually a fraction but sometimes written as a decimal or percentage.

To calculate the probability of something happening we use the following formula




















Example:  The probability of getting a 5 when rolling an ordinary dice is 1/6 because there is 1 number 5 on the dice out of 6 possible different answers.

The probability if getting an Ace from a standard pack of cards is 4/52 because there are 4 aces and 52 cards this can be simplified to 1/13.  You could also say that it is 1/13 because there are 13 cards in a suit and 1 of them is an ace.

Probability it doesn't happen
The probability of something not happening is 1 - the probability it does.  This is because either that thing is going to happen or it will not happen and so it covers all possibilities and together they equal 1.

Example:  The probability it will rain tomorrow is 0.56 so the probability it won't rain is 1 - 0.56 = 0.44

Experimental Probability and Relative Frequency
Probability can be used to predict results or to see if something is fair.  For example if I flip a coin 10 times theoretically we should get 5 heads and 5 tails but in reality we may get 7 heads and 3 tails.  From 10 results this may not seem odd, but if we flipped a coin 1000 times and got 700 heads and 300 tails you may think the coin is biased.

Relative frequency is the probability that an experiment produces.  For example above where I flipped my coin 10 times the theoretical probability of a head is 0.5 but in the experiment I got a head 7 out of 10 times so the relative frequency or experimental probability is 0.7.