Probability > Tree diagramsTheory
Many probability experiments can be described in terms of the random drawing of coloured balls from a vase. You call this a vase model. For each vase model you can construct a tree diagram to calculate probabilities. It is important to differentiate between the following two types of model:
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drawing with replacement: after drawing one ball from the vase you put this ball back into the vase and mix again. Only then do you draw the following ball. The tree then gives you `P(text{2 green}) = P(GG) = 2/5*2/5` `P(text{green and red}) = P(GR text{ or } RG) = 2/5*3/5 + 3/5*2/5` |
drawing without replacement: after drawing one ball from the vase you do not put it back in the vase. You immediately draw the next ball. (You may also draw two balls at the same time.)
`P(text{2 green}) = P(GG) = 2/5*1/4` `P(text{green and red}) = P(GR text{ of } RG) = 2/5*3/4 + 3/5*2/4` |
You can use a vase model to construct a tree diagram in many situations. You always multiply the probabilities along a certain route from the start of the tree. Because balls are being drawn, your tree will have "layers". THe number of layers is equal to the number of balls drawn.