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What you need to know
What you need to know:
Probability is the study of how likely, or probable, things are to happen. We express probabilities either as fractions, decimals, or percentages, and they always fall between 0 and 1, where 0 represents total impossibility and 1 represents total certainty.
The more interesting questions in probability come from asking the likelihood of not just one event happening but a series of events. One of the most useful tools we have of expressing a situation like this is the tree diagram. A tree diagrams is made of “branches”, and each branch represents an outcome, with the probability of that event written directly above/below the branch. You are required to know how to construct a tree diagram from information given in the question, and then use that tree diagram to determine the possibility of certain outcomes. You should be familiar with the “and/or” rule of probability. It tells us to multiply probabilities when we need several things all to happen (this is “and”) and add probabilities when we only require any one of several outcomes (this is “or”), and you should understand that in terms of tree diagrams, this means you multiply along the branches, and then add vertically.
It is important that you understand whether you’re working with independent events (the next event isn’t affected by the outcome of the last one, e.g. coin flips) or dependent events (the next event is affected by the outcome of the last one, e.g. picking coloured balls out of a bag without replacing them), and how this effects the probabilities at each step of your tree diagram. An example of a tree diagram is seen below.
If you are on the higher course, then you are also required to work with conditional probability; the likelihood of an outcomes given that we know something else has already happened, e.g. the chance that it will snow tomorrow given that we know it’s going to be 3 degrees Celsius. This type of probability comes into play when dealing with dependent events, and tree diagrams are extremely useful for helping us find conditional probabilities, so its important to know them well.
Probability and Tree Diagrams Revision and Worksheets
For GCSE Maths tutors in Harrogate to London, the probability revision materials and probability tree resources on this page will help you to form a comprehensive revision bank of questions. You may also want to use the probability worksheets as homework or in some cases refresher sessions. For more exceptional GCSE Maths resources visit our GCSE Maths 9-1 resource page.
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