# GRE Subject Test: Math : Probability & Statistics

## Example Questions

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### Example Question #1 : Axioms Of Probability

A student has 14 piece of gum, 3 are spearmint, 5 are peppermint, and the rest are cinnamon. If one piece of gum is chosen at random, which of the following is NOT true.

The probability of picking a spearmint is .

The probability of picking a cinnamon is .

The probability of picking a spearmint or a cinnamon is .

The probability of not picking a cinnamon is .

The probability of picking a cinnamon or a peppermint is .

The probability of picking a spearmint or a cinnamon is .

Explanation:

The probability of picking a spearmint or a cinnamon is the addition of probability of picking a spearmint and the probability of picking a cinnamon

not

### Example Question #1 : Sample Spaces

If I toss a coin 3 times, how many times will I roll at least one head?

None of the Above

Explanation:

Step 1: We need to find out how many outcomes there will be.
If we roll a coin three times, there are  outcomes.
If we roll a coin  times, there will be  outcomes.

Step 2: Find all the outcomes.

The outcomes here are: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.

Step 3: In the list of outcomes, count how many times the letter H appears at least once.

The letter "H" appears in HHH, HHT, HTH, HTT, THH, THT, and TTH.

The letter "H" appears in  of the  outcomes.

The probability of getting at least one H in the outcomes in Step 2 is .

### Example Question #1 : Sample Spaces

How many different combinations can i have when flipping a coin three times?

Explanation:

Step 1: Let's answer a smaller problem. How many ways can I toss one coin?

There are two ways, either I get Heads or Tails.

Step 2: How about two coins?

There are four ways... They are, HH, HT, TH, and TT

Step 3: How many different combinations for three coins?
Let's List them:
HHH, HHT, HTH, THH, TTT, THT, TTH, HTT

There are  different combinations.

### Example Question #1 : Mean

Find the mean of the following set of numbers:

Explanation:

The mean can be found in the same way as the average of a group of numbers. To find the average, use the following formula:

So, if our set consists of

We will get our mean via:

### Example Question #1 : Statistics

The mean of four numbers is .

A: The sum of the four numbers.

B:

Can't be determined from the given information.

Quantity A is greater.

Quantity B is greater.

Both are equal.

Both are equal.

Explanation:

To find the sum of the four numbers, just multiply four and the average. By multiplying the average and number of terms, we get the sum of the four numbers regardless of what those values could be.

Since Quantity A matches Quantity B, answer should be both are equal.

### Example Question #1 : Statistics

Mean of  is  are all positive integers.  is between  and  inclusive.

A: Mean of .

B: Mean of

Quantity A is greater.

Can't be determined from the information above.

Both are equal.

Quantity B is greater.

Can't be determined from the information above.

Explanation:

Let's look at a case where .

Let's have  be  and  be . The sum of the three numbers have to be  or

The average of  is  or . The avergae of  is  or .

This makes Quantity B bigger, HOWEVER, what if we switched the  and  values.

The average of  is still  or . The avergae of  is  or .

This makes Quantity A bigger. Because we have two different scenarios, this makes the answer can't be determined based on the information above.

### Example Question #1 : Other Topics

If  and are positive integers from  inclusive, then:

A: The mean of

B: The mean of

Can't be determined from the information above

Both are equal

Quantity B is greater

Quantity A is greater

Can't be determined from the information above

Explanation:

Let's add each expression from each respective quantity

Quantity A:

Quantity B:

Since  we will let  and . The sum of Quantity A is  and the sum of Quantity B is also . HOWEVER, if  was , that means the sum mof Quantity B is . With the same number of terms in both quantities, the larger sum means greater mean. First scenario, we would have same mean but the next scenario we have Quantity B with a greater mean. The answer is can't be determined from the information above.

### Example Question #2 : Other Topics

John picks five numbers out of a set of seven and decides to find the average. The set has

A: John averages the five numbers he picked from the set.

B:

Can't be determined from the information above

Quantity B is greater

Quantity A is greater

Both are equal

Quantity B is greater

Explanation:

To figure out which Quantity is greater, let's find the highest possible mean in Quantity A. We should pick the  biggest numbers which are . The mean is . This is the highest possible mean and since Quantity B is  this makes Quantity B is greater the correct answer.

### Example Question #1 : Probability & Statistics

Find the mean.

Explanation:

To find the mean, add the terms up and divide by the number of terms.

### Example Question #2 : Probability & Statistics

Find   if the mean of  is .

Explanation:

To find the mean, add the terms up and divide by the number of terms.