### Home > MC1 > Chapter 10 > Lesson 10.1.1 > Problem10-10

10-10.

Tom keeps all his favorite marbles in a special leather bag. Right now the bag holds five red marbles, four blue marbles, and three yellow marbles.

1. If he randomly chooses one marble to give to a friend, what is the probability that it is blue?

2. Tom does not really want to give away blue marbles and would like to change the probability that he chooses a blue marble to $\frac { 1 } { 10 }$. How many marbles that are not blue could he add to the bag so that the probability of choosing a blue marble becomes $\frac { 1 } { 10 }$?

The probability of picking a certain marble is the same as the possible number of desired outcomes in comparison to the number of all possible outcomes.

In this case, picking a blue marble is the desired outcome and the total number of marbles is the number of total possible outcomes.
Can you write down this probability?

$\text{The probability is }\frac{4}{12}=\frac{1}{3}$

$\text{If we know that there are four blue marbles,}$

$\text{what total number of marbles would make the ratio equivalent to }\frac{1}{10}?$

Can you set up a probability and solve it to find the total number of marbles?

$\frac{4}{x}=\frac{1}{10}$

Once you find the total number of marbles, be sure to subtract the original number of marbles in the bag (12).
This way, you will know how many marbles Tom has to add to the bag!