'Or' probabilities

Last updated: 24 Nov 2008

The probability that one or other of two exclusive outcomes occurring can be found be adding their individual probabilities.

Example with a die

What is the probability that when a 6 sided die is thrown that the result is prime.

The prime numbers in the range 1–6 are 2, 3 and 5, so

mathematical expression

Example with a jar

A jar contains 2 red balls and 4 green balls. If two balls are selected at random then what is the probability that they are the same color?

The probability that both balls selected are the same color is the probability that they are both red Or that they are both green.

P(two the same colour) = P(two red) + P(two green)

We already know that the probability that both are green is mathematical expression (see the jar example on the previous page).

And we can work out the probability that both are red.

mathematical expression

Putting this information together we can say that.

mathematical expression

So the probability that both balls picked out are the same color is mathematical expression.

Next page: Summary of permutations, combinations and probability

Comments (1):

  1. If I were to understand correstly:
    State Pick 3 lotto is a Permutation equation (3 in the right order).
    State Powerball is a Combination equation (any combination of a set range).

    mattm963 on 13 Jan 2010 (permalink)

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