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?

   Hint 1(a):

   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.

   Hint 2(a):

   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?

   Answer:

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

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 $\frac { 1 } { 10 }$?

   Hint 1(b):

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

   Hint 2(b):

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

   Hint 3(b):

   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!