Introduction
Probability is measured on a scale of fractions. You can, and people do, of course, use percentages or decimals as well as fractions to express a probability. Ratios such as used by bookmakers to express odds are not used in probability, although it is often thought that they should. The odds are not a probability of judging a winner, they are a tool to try and make sure the bookmaker makes a profit on the event - they are essentially a popularity poll rather than a scientific measure of likely outcomes.
A probability of 0 represents something that will not happen. The chance that the sun will not rise tomorrow. The chance that if you toss a coin on Earth it won't come down, or that it will come down and balance on edge.
Similarly a probability of 1 represents something that is sure to happen. The sun will rise tomorrow (it might hide behind clouds, but it will rise, at least in the foreseeable future), a coin will land if tossed. At least one student will graduate from the University of York this year and so on.
Other probabilities lie in between these extremes. If you toss a coin the chances of getting a head are ½ or 0.5 or 50%. If you roll a standard die (numbered 1-6 and no bias) there is a 1/6 chance of getting a 6.
If all the outcomes are equally likely, and they almost certainly are in the questions you will see on this subject, then you can work out the probability of a certainly outcome by working out the successful outcomes and dividing by the total outcomes. For example, there is a type of die called an average die. It has 6 sides, numbered 2, 3, 3, 4, 4, 5. The chance of rolling a 5 is 1/6 (one success (5) and 6 possible outcomes). The chance of rolling a 4 or 5 is ½: there are 3 success, two 4's and one 5, and 6 possible outcomes. 3/6 = ½
A bit more detail
The chances of something happening and it not happening should always add up to 1. You can use this to calculate harder problems where it may be easier to calculate the chances of something NOT happening.
If you know the probability of two events happening and you need to calculate the probability that A happens OR B happens, you add the probabilities together. The probability of getting a 5 or a 6 on a normal die is 1/6 + 1/6 = 1/3
If you know the probability of two events happening and you need to calculate the probability that they both happen (A AND B happen) then you multiply the probabilities. The probability of getting 2 6's if you roll 2 die is 1/6 X 1/6 = 1/36.
Complex probabilities and tree diagrams
You are fairly likely, if you take a test that includes probabilities, to be faced with a multi-part problem. If you can clearly visualise the calculations you can simply work this out using fraction or decimal multiplication. However, many people find that tree diagrams can help with this. There is an excellent description of this on the Probability Tree Diagram page.
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