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

## 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?

Explanation:

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?

Explanation:

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?

Explanation:

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?

Explanation:

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.)

Explanation:

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?

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 #27 : Outcomes

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

Explanation:

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?

Explanation:

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?

Explanation:

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?