• From: Kate
  • Date: 18 Feb 1999
  • Subject: Adding Probabilities for 'OR'-Type Questions

My teacher says that if you have an 'OR'-type question, you should add the probabilities together. But I had the question:

When two dice are rolled, what is the probablility of getting a double or a 6?
And I know that P(double) = 6/36 and P(6) = 5/36. Why is the answer not 11/36 ?

Maths Help suggests:

You can add two probabilies, but only if the events are mutually exclusive.

Events are mutually exclusive if
they cannot both occur at the same time.

Possibility Space Diagram The two events 'Getting a double' and 'Getting a 6' are not mutually exclusive, so their probabilities cannot be added together.

Have a look at the possibility space diagram. You will see the two events indicated.

Note the overlap of the '6' outcomes with the 'double' outcomes.

This clearly happens when the '6' is gained from a double '3'.

There are 10 outcomes which match the question, and so the correct probability is 10/36, which is equivalent to 5/18 .

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