# ISEE Lower Level Quantitative : Probability

## Example Questions

### Example Question #1 : Outcomes

Find the probability of an outcome. Express the outcome as fraction, reduced to its lowest terms.

Mr. Thomas went to a car lot to buy a new car. Of the 68 cars on the lot, 22 were black, 16 were silver, 8 were white, 12 were blue, and 10 were red.  What is the probability that Mr. Thomas will buy a blue car?

Explanation:

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

Since there are 12 blue cars (part) out of 68 cars in all (total possible) the fraction looks like this:

If you reduce the fraction by 4 (because the numerator and the denominator are both divisible by 4 which makes 4 the GCF (greatest common factor), it becomes:

### Example Question #2 : How To Find The Probability Of An Outcome

A bag of marbles contains  green marbles,  blue marbles, and  red marbles.

If  marbles are taken from the bag on each draw, what is the greatest possible amount of draws that can occur without drawing a red marble?

draws

draws

draws

draws

draws

draws

Explanation:

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.

### Example Question #2 : Probability

Mikey has a box filled with cookies. He has 6 chocolate chip cookies, 4 sugar cookies, and 2 oatmeal raisin cookies. What is the chance that Mikey picks a sugar cookie out of the box?

Explanation:

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!

### Example Question #1 : Outcomes

Sofia has a pizza pie with 8 slices. 4 slices have pepperoni, 3 slices have mushrooms and 1 slice has olives. If Sofia randomly picks a piece of pizza to eat, what is the chance that the slice of pizza has mushrooms on it?

Explanation:

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!

### Example Question #1 : Probability

Sarah, Mitch, and Ben are going to a concert. If they are seated in a row of , what fraction represents the probability Sarah will be seated in the middle of the row?

Explanation:

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 .

### Example Question #2 : Outcomes

Shannon has a box with 9 shirts inside. 4 shirts are pink, 3 shirts are yellow, 1 shirt is red, and 1 shirt is green. What is the probability that Shannon will randomly pick a pink shirt from the box?

Explanation:

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!

### Example Question #3 : Outcomes

Tucker is going fishing at a local pond with 15 fish. 5 fish are tuna, 4 fish are salmon, 3 fish are yellowtail, and 3 fish are trout. What is the chance that the first fish Tucker catches will be a tuna or a trout?

Explanation:

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!

### Example Question #11 : Data Analysis And Probability

Jenny buys two dozen donuts from the bakery. If 12 donuts are glazed, 6 donuts are jelly, 4 donuts are powdered and 2 donuts are plain, what is the chance that she will randomly pick a powdered donut from the box?

Explanation:

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!

### Example Question #11 : Outcomes

Mikey has a box of chocolates. 5 chocolates have a caramel filling, 6 chocolates have an almond filling, 3 chocolates have no filling, and 1 chocolate has a cherry filling. If Mikey selects a chocolate from the box at random, what is the chance that he selects a chocolate with a filling?

Explanation:

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!

### Example Question #11 : Probability

Niall has a box of 6 scarves. 3 scarves are purple, 2 scarves are blue, and 1 scarf is white. What is the chance that Niall will randomly pick a blue scarf from the box?