# ISEE Lower Level Quantitative : How to find the probability of an outcome

## Example Questions

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### Example Question #41 : Data Analysis And Probability

There are  marbles in a bag:  are blue,  are white,  are yellow, and  are green. What is the probability of choosing blue or green at random?

Explanation:

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  .

### Example Question #42 : Outcomes

A bag contains  red socks and  purple socks. What is the chance that I pick a purple sock from the bag?

Explanation:

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!

### Example Question #43 : Outcomes

Mr. Brown has  red shirts,  blue shirts,  yellow shirts, and  green shirts. If he selects a shirt randomly, what color shirt has a  in  chance of being chosen?

Red

Blue

Green

Yellow

Green

Explanation:

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.

### Example Question #42 : Data Analysis And Probability

There is a raffle for a basket of cookies. Bill buys 3 tickets, Julie buys 2 tickets, Rob buys 4 tickets, and 5 other people buy 2 tickets each. What are the chances that Rob will win the raffle?

Explanation:

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 .

### Example Question #45 : Outcomes

Ebony has a drawer of socks with five different colors: green, purple, black, white, and yellow. The probability of her choosing a white sock is 3 out of 7. Which combination of socks is possible?

6 white socks and 14 other socks

3 white socks and 7 other socks

1 white sock and 4 other socks

9 white socks and 12 other socks

7 white socks and 21 other socks

6 white socks and 14 other socks

Explanation:

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.

### Example Question #46 : Outcomes

There are 64 students in a science class. If there are 24 boys, what is the ratio of the number of girls to the total number of students in the science class?

Explanation:

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

### Example Question #47 : Outcomes

Mary has a bag with  cookies.  cookies are chocolate chip,  cookies are sugar, and  cookies are oatmeal raisin. What is the chance that Mary randomly selects a sugar cookie from the bag?

Explanation:

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 .

### Example Question #48 : Outcomes

Caroline has 3 books, 2 pencils, 1 candy, and 4 binders in her backpack. If she randomly chooses an item from her backpack, what is the probability of her randomly picking out a pencil?