This one is an interesting teaser that includes a few different concepts:

A bowl contains five marbles, labeled 1 through 5. Paul randomly selects one of the marbles, records its number, and places it back into the bowl. Then, Susie randomly selects a marble from the bowl, records that number and places it back. What is the probability (in terms of a fraction) that the sum of their selected numbers will be an even number?

ANSWER:

From the Miscellaneous Math module, probability is defined as:     # of desired outcomes                                                                                                                                                                                                                # of total possible outcomes

Using the multiplication rule, we can find the total possible outcomes. (Note that since Paul is putting his choice back in the bowl, Susie also has 5 choices.) Multiply the number of choices for Paul times the number of choices for Susie, or    (5)(5)   =    25 total possible outcomes.

As discussed in the Arithmetic module, it helps to remember that an even plus an even equals an even number, and an odd plus an odd also equals an even number. (An even plus an odd equals an odd number, so we don't have to count those.) First, we can quickly list the number of ways Paul and Susie would both draw even numbers out of their choices of 1 through 5.

Paul    Susie

2          2

2          4

4          2

4          4

Or, we could do this using the multiplication rule as well:     (2 ways)(2 ways)    =     4 ways to get an even result

Now do the same with two odd numbers:

Paul    Susie

1          1

1          3

1          5

3          1

3          3                      OR,     (3)(3)   =     9 ways to get an even #

3          5

5          1

5          3

5          5

Since there are 13 ways to get an even number, our final answer is:         13/25

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