### All GMAT Math Resources

## Example Questions

### Example Question #1 : Calculating Probability

Two dice are rolled. What is the probability that the sum of both dice is greater than 8?

**Possible Answers:**

**Correct answer:**

There are 36 possible outcomes (). 10 out of the 36 outcomes are greater than 8: (6 and 3)(6 and 4)(6 and 5)(6 and 6)(5 and 4)(5 and 5)(5 and 6)(4 and 5)(4 and 6)(3 and 6).

### Example Question #2 : Calculating Probability

Among a group of 300 people, 15% play soccer, 21% play baseball, and 9% play both soccer and baseball. If one person is randomly selected, what is the probability that the person selected will be one who plays baseball but NOT soccer?

**Possible Answers:**

**Correct answer:**

Since there are 300 people, people play baseball and of those people play both baseball and soccer. Therefore, there are people who play baseball but not soccer.

Probability:

### Example Question #3 : Calculating Probability

If a die is rolled twice, what is the probability that it will land on either 2 or an odd number both times?

**Possible Answers:**

**Correct answer:**

probability on one roll:

for both times=

### Example Question #4 : Calculating Probability

What is the probability of sequentially drawing 3 aces from a deck or regular playing cards when the selected cards are not replaced?

**Possible Answers:**

**Correct answer:**

The probability of drawing an ace first is or .

Assuming an ace is the first card selected, the probability of selecting another ace is or .

For the third card, the probability is or .

To calculate the probability of all 3 events happening, you must multiply the probabilities:

### Example Question #5 : Calculating Probability

How many even four-digit numbers larger than 4999 can be formed from the numbers 2, 4, 5, and 7 if each number can be used more than once?

**Possible Answers:**

**Correct answer:**

Since the number must be larger than 4999, the thousand’s digit has to be 5 or 7. We are also told that the number must be even. Thus, the unit’s digit must be 2 or 4. The middle digits can by any of the numbers 2,4,5, or 7. Therefore, we have a total of possibilities.

### Example Question #4 : Calculating Probability

What is the probability of rolling an even number on a standard dice?

**Possible Answers:**

**Correct answer:**

A standard dice has 6 faces numbered .

There are even numbers, , divided by the total number of faces:

### Example Question #5 : Calculating Probability

Shawn is competing in an archery tournament. He gets to shoots three arrows at a target, and his best two shots count.

He hits the bullseye with 40% of his shots. What is the probability that he will hit the bullseye at least twice out of the three times?

**Possible Answers:**

**Correct answer:**

There are three scenarios favorable to this event.

1: He hits a bullseye with his first two shots; the third shot doesn't matter.

The probability of this happening is

2: He hits a bullseye with his first shot, misses with his second shot, and hits with his third shot.

The probability of this happening is

3: He misses with his first shot and hits a bullseye with his other two shots.

The probability of this happening is

Add these probabilities:

### Example Question #2 : Calculating Probability

A store uses the above target for a promotion. For each purchase, a customer gets to toss a dart at the target, and the outcome decides his prize. If he hits a pink region, he gets nothing; if he hits a red region, he gets a 10% discount on a future purchase; if he hits a green region, he gets a 20% discount; if he hits a blue region, he gets a 40% discount.

Assume a customer hits the target and no skill is involved. What are the odds against him getting a discount?

**Possible Answers:**

**Correct answer:**

The customer gets a discount if he does not hit a pink region. There are ten out of twenty ways to hit a pink region and ten to not hit one - this makes the odds 10 to 10, or, in lowest terms, 1 to 1 against a discount.

### Example Question #3 : Calculating Probability

It costs $10 to buy a ticket to a charity raffle in which three prizes are given - the grand prize is $3,000, the second prize is $1,000, and the third prize is $500. Assuming that all of 1,000 tickets are sold, what is the expected value of one ticket to someone who purchases it?

**Possible Answers:**

**Correct answer:**

If 1,000 tickets are sold at $10 apiece, then $10,000 will be raised. The prizes are $3,000, $1,000, and $500, so $4,500 will be given back, meaning that the 1,000 ticket purchasers will collectively lose $5,500. This means that on the average, one ticket will be worth

This is the expected value of one ticket.

### Example Question #4 : Calculating Probability

Daria has 5 plates: 2 are green, 1 is blue, 1 is red, and 1 is both green and blue. What is the probability that Daria randomly selects a plate that has blue OR green on it?

**Possible Answers:**

**Correct answer:**

The easiest way to solve this is by using the complement. Only one of the five plates is NOT blue or green. So of the plates are NOT blue or green. Therefore of the plates are blue or green.

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