SOLUTION: suppose a single fair die is rolled. find the probability that it is a 6, given that it is an even number

Two ways to a conditional probability: 

1. By reducing the sample space
2. By formula

First, let's do it by reducing the sample space:

The original sample space is {1,2,3,4,5,6}

We are given that it is an even number.

So remove every outcome from the sample space that does not jibe
with what is given.  So we remove the 1, the 3 and the 5.  So
the reduced smaple space is {2,4,6}

So the conditional probability of 6 is 1 out of 3 or .

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Now we'll do it by the formula method using only the original sample space:

 

 

Probability that it is 6 and even = 1 way out of 6 or 

Probability that it is even = 3 ways out of 6 or  or 



Edwin