### All ISEE Lower Level Quantitative Resources

## Example Questions

### Example Question #11 : How To Find The Probability Of An Outcome

There are 10 marbles in a bag:

7 red

2 blue

1 yellow

What is the probability of choosing a red ball out of the bag?

**Possible Answers:**

**Correct answer:**

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:

### Example Question #22 : Outcomes

Joey has 10 shirts on his bed. 4 shirts are blue, 3 shirts are purple, 2 shirts are green, and 1 shirt is white. What is the chance that Joey randomly picks a purple shirt from the shirts on his bed?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #23 : Outcomes

Express the probability as a fraction.

Nija has 7 marbles. There are 2 red, 3 blue, and 2 yellow. What is the probablilty that Nija will choose a red marble?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #24 : Outcomes

In a restaurant there are two managers, three workers, and twelve guests. What is the probability that a person chosen at random is a worker?

**Possible Answers:**

**Correct answer:**

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:

### Example Question #22 : Data Analysis And Probability

A ring toss game has 25 bottles, 5 of which are yellow. If you toss a ring around a yellow bottle, you win the grand prize. What is the probability of winning the grand prize? (Give the fraction in simplest form.)

**Possible Answers:**

**Correct answer:**

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.

### Example Question #26 : 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?

**Possible Answers:**

**Correct answer:**

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 #27 : Outcomes

Selena has a standard deck of cards. What is the chance that she randomly selects a red card from the deck?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #28 : Outcomes

Josh has cards in his hand. These cards are each red, yellow, or blue. If of the cards are red and are yellow, what is the probability of drawing a blue card?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #29 : Outcomes

A piggy bank contains an assortment of quarters, dimes, nickels, and pennies. Assuming all coins are equally likely to be picked, if there are pennies, nickels, dimes, and quarters, what is the probability of drawing a quarter out of the bank?

**Possible Answers:**

**Correct answer:**

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

### Example Question #30 : Outcomes

In a washing machine, there are blankets, shirts, and pants. What is the probability of taking out a peice of clothing first?

**Possible Answers:**

**Correct answer:**

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 .

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