Probability & Statistics

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GRE Quantitative Reasoning › Probability & Statistics

Questions 1 - 10
1

What is the mean of

Explanation

Step 1: Find the sum of the numbers

Step 2: Find how many numbers

There are numbers..

Step 3: Divide the sum by how many numbers they are...This division gives us the mean..

2

What is the range of the set of numbers: ?

Explanation

Step 1: Arrange the numbers in the set from smallest to largest:

After we arrange, we get: .

Step 2: To find the range, subtract the largest number from the smallest number.

The range of the data set is .

3

Daisy wants to arrange four vases in a row outside of her garden. She has eight vases to choose from. How many vase arrangements can she make?

Explanation

For this problem, since the order of the vases matters (red blue yellow is different than blue red yellow), we're dealing with permutations.

With selections made from potential options, the total number of possible permutations(order matters) is:

4

What is the mean of:

Explanation

Step 1: Take the sum of all numbers in the set...

Step 2: Count how many elements are in the set...

There are numbers

Step 3: To find the mean, divide the sum by the number of elements..

The mean is

5

Evaluate:

Explanation

Step 1: Write in multiplication form:

Step 2: Multiply Out

6

What is the mean of:

Explanation

Step 1: Find the sum of the numbers

Step 2: Count how numbers there are:

There are numbers..

Step 3: Divide Sum by how many numbers

7

What is the mean of

Explanation

Step 1: Find the sum of the numbers in the set...

Step 2: Count how many numbers are in the set..

There are 10 numbers...

Step 3: Divide the total sum by how many numbers...

So,

8

There are 12 boys in a football competition, the top 3 competitors are awarded with an trophy. How may possible groups of 3 are there for this competition?

Explanation

This is a permutation. A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as

There are possible groups of 3.

9

Mohammed is being treated to ice cream for his birthday, and he's allowed to build a three-scoop sundae from any of the thirty-one available flavors, with the only condition being that each of these flavors be unique. He's also allowed to pick different toppings of the available , although he's already decided well in advance that one of them is going to be peanut butter cup pieces.

Knowing these details, how many sundae combinations are available?

Explanation

Because order is not important in this problem (i.e. chocolate chip, pecan, butterscotch is no different than pecan, butterscotch, chocolate chip), it is dealing with combinations rather than permutations.

The formula for a combination is given as:

where is the number of options and is the size of the combination.

For the ice cream choices, there are thirty-one options to build a three-scoop sundae. So, the number of ice cream combinations is given as:

Now, for the topping combinations, we are told there are ten options and that Mohammed is allowed to pick two items; however, we are also told that Mohammed has already chosen one, so this leaves nine options with one item being selected:

So there are 9 "combinations" (using the word a bit loosely) available for the toppings. This is perhaps intuitive, but it's worth doing the math.

Now, to find the total sundae combinations—ice cream and toppings both—we multiply these two totals:

10

Mohammed is being treated to ice cream for his birthday, and he's allowed to build a three-scoop sundae from any of the thirty-one available flavors, with the only condition being that each of these flavors be unique. He's also allowed to pick different toppings of the available , although he's already decided well in advance that one of them is going to be peanut butter cup pieces.

Knowing these details, how many sundae combinations are available?

Explanation

Because order is not important in this problem (i.e. chocolate chip, pecan, butterscotch is no different than pecan, butterscotch, chocolate chip), it is dealing with combinations rather than permutations.

The formula for a combination is given as:

where is the number of options and is the size of the combination.

For the ice cream choices, there are thirty-one options to build a three-scoop sundae. So, the number of ice cream combinations is given as:

Now, for the topping combinations, we are told there are ten options and that Mohammed is allowed to pick two items; however, we are also told that Mohammed has already chosen one, so this leaves nine options with one item being selected:

So there are 9 "combinations" (using the word a bit loosely) available for the toppings. This is perhaps intuitive, but it's worth doing the math.

Now, to find the total sundae combinations—ice cream and toppings both—we multiply these two totals:

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