Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are  blue and green marbles and a total of  chocolates. This is represented as the fraction: . This can be reduced to . The answer is  .

To find the probability of picking a purple sock from the bag of socks, we need to set up a fraction like this: . The problem tells us that we have  purple socks, so we can put that on the top of the fraction. The total number of socks is equal to  purple socks +  red socks, giving us a sum of  (which goes on the bottom of the fraction). That gives us a  chance of picking a purple sock from the bag!

Recall what a probability is:

Now, we have a total number of  outcomes because that is the number of shirts Mr. Brown has to choose from.

We can then set up the following ratio:

Notice that you multiply  by  to get . The value for  then should be . Out of all the shirts Mr. Brown has to choose from, the only color shirt that he has  of is green.

If Bill buys 3 tickets, Julie buys 2 tickets, Rob buys 4 tickets, and 5 other people buy 2 tickets each, there are a total of 19 tickets:

Thus, the chance of Rob winning is .

We are looking at probability and proportion in this problem.

If there is a 3 out of 7 chance of getting a white sock, this can be expressed as  or 3:7.

Then, we must find an equivalent combination, which would be 6:14.

We are given the ratio of boys in the class, which is .

First, we must reduce that fraction by finding the greatest common denominator, which is 8.

The fraction is then reduced to .

We are looking for the ratio of girls in the gym class.

So we subtract 

. 

This leaves us with our answer of 

To find the probability of Mary picking a sugar cookie from the bag of cookies, we need to set up a fraction like this: .

The problem tells us that Mary has  sugar cookies, so we can put that on the top of the fraction. The problem also tells us that Mary has  total cookies, so we can put that on the bottom of the fraction. That gives Mary a  chance of picking a sugar cookie.

Since  is not an answer choice, we need to reduce the fraction. To reduce a fraction means to divide the top (numerator) and the bottom (denominator) by a common factor that both numbers share. The numbers  and  both have a common factor of , so we can divide the top and the bottom by  to get the correct answer of .

Probability is all about part and whole. First, add up how many items are in her backpack (10). Then, notice how many pencils she has (2). Put the part over the whole, which gives you .

This can be further simplified/reduced to .