GRE Subject Test: Math : Probability & Statistics

Study concepts, example questions & explanations for GRE Subject Test: Math

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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.

Possible Answers:

The probability of picking a cinnamon is .

The probability of picking a spearmint or a cinnamon is .

The probability of picking a cinnamon or a peppermint is .

The probability of not picking a cinnamon is .

The probability of picking a spearmint is .

Correct answer:

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 : Probability & Statistics

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

Possible Answers:

None of the Above

Correct answer:

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 : Other Topics

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

Possible Answers:

Correct answer:

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:

 

Possible Answers:

Correct answer:

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:

So our answer is

Example Question #2 : Other Topics

The mean of four numbers is .

A: The sum of the four numbers.

B: 

Possible Answers:

Can't be determined from the given information.

Quantity B is greater.

Quantity A is greater.

Both are equal.

Correct answer:

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 #3 : Other Topics

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

A: Mean of .

B: Mean of 

Possible Answers:

Both are equal. 

Quantity B is greater.

Quantity A is greater.

Can't be determined from the information above.

Correct answer:

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 #4 : Other Topics

If  and are positive integers from  inclusive, then:

A: The mean of 

B: The mean of 

Possible Answers:

Can't be determined from the information above

Quantity A is greater

Quantity B is greater

Both are equal

Correct answer:

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 #1 : Mean

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: 

Possible Answers:

Can't be determined from the information above

Quantity B is greater

Quantity A is greater

Both are equal

Correct answer:

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 #6 : Other Topics

Find the mean.

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 : Other Topics

Find   if the mean of  is .

Possible Answers:

Correct answer:

Explanation:

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

 Then add the numerator.

 Cross-multiply.

 Subtract  on both sides.

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