'Or' probabilities

Last updated: 7 Aug 2008

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

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

The prime number is the range 1-6 are 2, 3 and 5, so

`P(text{die roll is prime}) = P(2) + P(3) + P(5)`

`P(text{die roll is prime}) = 1/6 + 1/6 + 1/6 = 1/2`

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 2/5 (see the jar example on the previous page).

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

`P(text{both red}) = P(text{first isred}) xx P(text{second is red})`

`P(text{both red}) = 2/6 xx 1/5 = 1/15`

Putting this information together we can say that.

`P(text{two the same colour}) = P(text{two red}) + P(text{two green})`

`P(text{two the same colour}) = 1/15 + 2/5 = 7/15`

So the probability that both balls picked out are the same color is 7/15.

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