Data Analysis and Probability - ISEE Lower Level Quantitative Reasoning

Card 0 of 1681

Question

What is the missing value of w in this sequence?

Answer

In this sequence, every subsequent number is 7 less than the preceding number. Given that the number that precedes w is 71, the value of w is . Therefore, 64 is the correct answer.

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Question

What is the value of n in the sequence below?

Answer

The numbers increase by 5. Given that the number before n is 20, the value of n is .

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Question

Bob recorded the number of red cars he saw out his office window every day. He recorded 15 more cars on Wednesday than on Friday.

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According to the chart, how many real life cars does each car picture represent?

Answer

Look at the chart and count how many more car pictures there are on Wednesday than on Friday: three red car pictures.

Divide the actual difference in the number of cars by the difference in the number of car pictures in the table: 15 3 = 5, which is the correct answer.

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Question

Eric has a 2 red shirts, 3 orange shirts, 4 purple shirts, and 1 pink shirt. If Eric randomly chooses a shirt, what are the chances that he selects a pink shirt?

Answer

First, add up all of the shirts.

\dpi{100} 2+3+4+1=10\ shirts

We then see that Eric has 1 pink shirt and 10 shirts from which to choose. Build a fraction with the number of pink shirts on top, and the total number of shirts on the bottom, \dpi{100} \frac{1}{10}.

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Question

Ten cards each have a number printed on them. Five have a 1 printed on them, three have a 2, and two have a 3. The cards are shuffled and a card is dealt. What is the probability that the card will not be a 3?

Answer

There are ten cards total, and eight cards that are not threes. This makes the probability of drawing a three

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Question

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?

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 .

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Question

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.)

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.

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Question

A magician holds in his bag 3 green balls, 4 red balls and 7 blue balls. What is the probability of drawing a red ball from the bag?

Answer

Probability = total number of possible outcomes/sample space.

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Question

If there are 2 blue marbles and 18 red marbles in a jar, what is the probability that Jeff will pick out a red marble?

Answer

First, add the total number of marbles, which is . There are 18 red marbles, so you set up a fraction .

If you simplify by dividing the numerator and denominator by 2, you get .

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Question

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?

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:

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Question

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?

Answer

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:

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Question

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?

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:

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Question

What is the next number in the series?

Answer

First, determine what the pattern is in the series. The pattern here is to multiply the previous number by 2 and then add 1. Therefore, multiply 47 by 2 (which is 94), and then add 1. The result is 95.

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Question

Casey has a bag containing red, yellow, blue, and green beads. There are equal numbers of red and blue beads, which comprise half the bag when combined. If there are 24 beads in the bag, what is the probability that Casey will select a blue bead?

Answer

There are beads in Casey's bag. We know that the red and blue beads make up half of the bag, so we divide by to find the total number of red and blue beads.

Since there is an equal number of red and blue beads, we divide by .

To find probability, we create a fraction with our desired outcome written as the numerator and the total possible outcomes written as the denominator:

Since and are divisible by , we must reduce the fraction.

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Question

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

Answer

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!

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Question

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?

Answer

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!

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Question

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?

Answer

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!

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Question

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?

Answer

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!

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Question

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?

Answer

Probability is all about part and whole. First, add up how many items are in her backpack (10). Then, notice how many pencils she has (2). Put the part over the whole, which gives you .

This can be further simplified/reduced to .

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Question

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?

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.

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