Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we want a red marble. Since there are  red marbles, we have  wanted outcomes. Since there is a total of  marbles, we have a total of  possible outcomes.

The probability then becomes the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we want a blue marble. Since there are  blue marbles, we have  wanted outcomes. Since there is a total of  marbles, we have a total of  possible outcomes.

The probability then becomes the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we want a green marble. Since there are  green marbles, we have  wanted outcomes. Since there is a total of  marbles, we have a total of  possible outcomes.

The probability then becomes the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we do not want a blue marble. This means that we are trying to find the proability of drawing either a red or a green marble. Since we have  red marbles and  green marbles, we have  wanted outcomes. Since there is a total of  marbles, we have a total of  possible outcomes.

The probability then becomes the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we do not want a green marble. This means that we are trying to find the proability of drawing either a blue or a green marble. Since we have  blue marbles and  red marbles, we have  wanted outcomes. Since there is a total of  marbles, we have a total of  possible outcomes.

The probability then becomes the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

First, write down the possible wanted outcomes:

Now, because there are  even numbers, we have  wanted outcomes.

Since we are choosing numbers between  and , inclusive, we have a  total outcomes.

The probability then can be written as the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

First, write down the possible wanted outcomes:

Now, because there are  numbers divisible by four, we have  wanted outcomes.

Since we are choosing numbers between  and , inclusive, we have a  total outcomes.

The probability then can be written as the following:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

First, write down the possible wanted outcomes:

Now, because there are  numbers that fit the criteria, we have  wanted outcomes.

Since we are choosing numbers between  and , inclusive, we have a  total outcomes.

The probability then can be written as the following:

The probability of an event not happening is one minus the probability it does happen.  

Since the probability of winning the game is , then the probability of not winning would be,

  .

To the probability of selecting a particular fish is the number of that fish divided by the total possible fish to choose from.  

The total is  gold fish plus  beta fish or .  

So the probability of selecting a beta fish is 

.