Question

A pencil 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. %

Answer 1

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%)