Apencil bag contains 24 red pencils, 15 blue pencils, and 8 green pencils. without looking, carrie selects a pencil, gives it to her friend, and then selects another pencil. what is the probability that carrie selected a blue pencil for her friend and a red pencil for herself? round to the nearest tenth of a percent. %

First of all, here is the formula that solves ALL probability problems.
Memorize this:

Probability =
       (number of different successful possibilities)
divided by
       (total number of all possibilities).

At the beginning, the pencil bag contains (24 + 15 + 8) = 47 pencils.

The first pencil Carrie will pull out is for her friend.  What's the probability
that it will be a blue one ?
There are 15 blue pencils in the bag, so out of the 47 total possible results,
15 of them would be successful.
So the probability of pulling a blue one is    15/47 .

Now, after that, she wants to pull out a red one for herself.  Notice that
there are only 46 pencils in the bag now.  And 24 of them are red.  So
the probability of pulling a red one is  24/46 .

The probability of BOTH events being successful is the product

                (15/47) x (24/46) .

It's time to pull out the calculator.

        (15/47) x (24/46) = 360/2162 = 0.1665  =  16.65%    (16.7%)