Probability

Probability trees


We can use probability trees to help understand probabilities even more.
Let's try an example ...

Imagine a town where 60% of the cat population are short haired cats and 40% are long haired cats.

Long haired cats have fleas with a probability of 35%, whereas short haired cats have of probability of 20% of having fleas.

Calculate the probability that a cat, picked at random has fleas.



So, there will be short haired cats & long haired cats with fleas.

The probability that a cat picked at random is short haired and has fleas is ...

                                               Probability = 60% x 20%

                                                                       = 12%


The probability that a cat picked at random is long haired and has fleas is ...

                                               Probability = 40% x 35%

                                                                       = 14%


To find the probability that a cat picked at random will have fleas we just add together these two values ...

In fact to calculate the probability that either event A will happen OR event B will happen we add the probability of each event together, so ...

Probability of event A OR event B happening = Probability of event A + Probability of event B

So, probability that a cat picked at random will have fleas = 12% + 14%

                                                                                                                      = 26%