To find the probability of an outcome, set up a fraction:

Since there are 7 red marbles (part) out of 10 marbles in all (total possible) the fraction looks like this: 

To find the probability of picking a purple shirt from the pile of shirts on Joey's bed, we need to set up a fraction like this:

The problem tells us that Joey has 3 purple shirts, so we can put that in the numerator. We are also told that the total number of shirts on Joey's bed is 10, so 10 goes on the bottom of the fraction. Therefore, Joey has a  chance of picking a purple shirt.

Probability can be expressed as a fraction:

Our fraction is .

Since there are 2 red marbles out of 7 total marbles, the probability of choosing a red marble is .

The total number of people in the room is the sum of all the different types of people:

The probability of choosing a worker is the number of workers divided by the total number of people. There are three workers and seventeen people in total:

To find the probability of an outcome, set up a fraction.

Since there are 5 yellow (part) out of 25 bottles (total possible) the fraction looks like this: .

Reduce the fraction by dividing the top and bottom by 5:

This is the probability of winning the grand prize.

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 .

To find the probability of Selena picking a red card from a standard deck of cards, we need to set up a fraction like this: .

A standard deck of cards has 52 cards, 26 of which are black and 26 of which are red. Our fraction looks like this:

We can reduce the fraction, since both numbers share a common factor.

Of the  cards Josh has in his hand,  are red and  are yellow. We need to figure out how many blue cards Josh must have in his hand. We are told that each of the cards in Josh's hand is either red, yellow, or blue, so if a card is not red or yellow, it is blue. Since  cards that are red or yellow, the rest of the cards must be blue. , so there must be  blue cards in Josh's hand. The total number of cards is , so the chance of drawing a blue card is .

Adding together all of the numbers,  total coins. Since there are  quarters, the probability of drawing a quarter is , which can be simplified to .

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  pieces of clothing and a total of  items in the washing machine. This is represented as the fraction: . This can be reduced to . The answer is .