There are  green marbles and  red marbles in the bag. Adding these amounts together gives  marbles in the bag that are not red. If all  of these were drawn before any red marble, this would require  draws at  marbles per draw (). Therefore, it is possible to draw up to  times without drawing a red marble.

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

The problem tells us that Mikey has 4 sugar cookies, so we can put that on the top of the fraction. The total number of cookies is equal to 6 chocolate chip cookies + 4 sugar cookies + 2 oatmeal raisin cookies, giving us a sum of 12 (which goes on the bottom of the fraction). That gives Mikey a  chance of picking a sugar cookie!

To find the probability of picking a mushroom slice from the pizza pie, we should set up a fraction like this: 

The problem tells us that we have 3 mushroom slices, so we can put that on the top of the fraction. The problem also tells us that we have 8 total slices in the pizza pie, so that can go on the bottom of the fraction. That gives Sofia a  chance of picking a mushroom slice!

The number of total possible arrangements of three items in a row is , or .

We can write out all the possible arrangments and count the number in which Sarah sits in the middle.

1) 

2) 

3) 

4) 

5) 

6) 

In  out of  possible arrangements, Sarah sits in the middle. Expressed as a fraction, this is , which is equivalent to .

To find the probability of picking a pink shirt from the box, we need to set up a fraction: . The problem tells us that Shannon has 4 pink shirts, so we can put that on the top of the fraction. The total number of shirts is 9, which goes on the bottom of the fraction. That gives Shannon a  chance of picking a pink shirt from the box!

To find the probability of Tucker catching a tuna or a trout, we need to set up a fraction like this: . The problem tells us that there are 5 tuna and 3 trout in the pond, so we can put 8 on the top of the fraction. The total number of fish in the pond is 15, so that goes on the bottom of the fraction. That gives Tucker an 8/15 chance of catching a tuna or trout!

To find the probability of picking a powdered donut from the box of donuts, we need to set up a fraction like this: . The problem tells us that we have 4 powdered donuts, so we can put that on the top of the fraction. The total number of donuts is 2 dozen, which is equal to 24 donuts (which goes on the bottom of the fraction). That gives Jenny a  chance of picking a powdered donut from the box!

To find the probability of Mikey selecting a piece of chocolate with a filling from the box of chocolates, we need to set up a fraction like this: .

The problem tells us that we have 5 chocolates with a caramel filling, 6 chocolates with an almond filling, and 1 chocolate with a cherry filling. We need to add them all together to find out how many chocolates have any type of filling, and place that number on top of the above fraction.

Now, we need to add 3 more to the above number because the box has 3 chocolates with no filling, and then use that new number as our denominator (on the bottom of the fraction). 

That gives Mikey a 12/15 chance of picking a filled chocolate from the box of chocolates!

To find the probability of picking a blue scarf from the box, we need to set up a fraction like this: . The problem tells us that Niall has 2 blue scarves, so we can put that on the top of the fraction. The problem also tells us that Niall has a total of 6 scarves, so we can put that on the bottom of the fraction. That gives Niall a  chance of picking a blue scarf from the box!

To find the probability of Harvey picking a rose from the bouquet of flowers, we need to set up a fraction like this: 

The problem tells us that Harvey has 3 roses, so we can put that on the top of the fraction. The problem also tells us that Harvey has 12 total flowers, so we can put that on the bottom of the fraction. That gives Harvey a  chance of picking a rose from the bouquet! 

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 3 and 12 both have a common factor of 3, so we can divide the top and the bottom by 3 to get the correct answer of .