Tuesday, 18 September 2012

Probability Tree and Multiplication of probabilities

Probability Tree

What is a Tree Diagram?
A widely used diagram in solving probability problems which comprises of a number of branches. Each branch leads to an outcome in the sample space. In the tree diagram, all the possible outcomes are fair and equally likely to occur.

What is Probability Tree?
In independent events, when the probabilities of different events are not equal, the value of each probability has to be written on the respective branch of the tree. This tree is then called as probability tree. The 'branches' of a probability tree represent outcomes which are mutually exclusive.

What multiplication of probabilities?
It is needed when a outcome has 2 factors affecting the probability, a dependent event. Multiplication of the probabilities in both experiments with the same object is needed to find the overall probability.
An example would be calculating the probability of getting 6 as the first number and 3 as the second number when a 6 sided equal fair dice is being rolled 2 times. 
First we will have to calculate the probability of getting 6 and 3 individually in each roll, which is also finding out the possibility of getting 6 as the outcome on the first roll. 
After that we have to calculate the probability of getting 3 as the second number AFTER getting 6 as the first outcome. So we will have to multiply the possibility of getting 3 with the possibility of getting 6 as the first outcome. 
So:  (1/6)x(1/6)=(2/36)=(1/18)

Example 15

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