A tree diagram is a clever way of mapping out the probably of one even happening after another. The probably of every branch coming from the same point has to sum to 1. To work out the probability of one event happening after another, you multiply both their individual probabilities together.

Example:

 

 

 

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A bag contains 4 red balls, 6 black balls. A ball is taken out of the bag at random and then replaced. Then another ball is taken out.

Notice how the ball is taken out at random, and then replaced - this is very important when working with tree diagrams to find out the probability of an outcome (This will be further discussed in problems involving independent & dependent events)

To draw a tree diagram, we need to consider the possibility of what ball we will get when one is taken out. Since there are 4+6 = 10 balls altogether.

So the probability of choosing a red ball is 2/5, a black ball is 3/5.  As the ball is replaced after it has been taken out, we still remain with 10 balls in the bag. so the probabilities of choosing each ball will be the same.

From the tree diagram below, we can see that each ball has its own 'branch' and above that branch is the probability of its outcome.

 

 

 

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AQA Unit 1 November 2011 (H) - Page 10, Question 8

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