GMAT Math : Calculating probability

Study concepts, example questions & explanations for GMAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Data Interpretation

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

Possible Answers:

\small \frac{7}{18}\(\displaystyle \small \frac{7}{18}\)

\small \frac{5}{9}\(\displaystyle \small \frac{5}{9}\)

\small \frac{5}{18}\(\displaystyle \small \frac{5}{18}\)

\small \frac{1}{8}\(\displaystyle \small \frac{1}{8}\)

Correct answer:

\small \frac{5}{18}\(\displaystyle \small \frac{5}{18}\)

Explanation:

There are 36 possible outcomes (\(\displaystyle 6\times 6=36\)). 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).

\small \frac{10}{36}\ =\ \frac{5}{18}\(\displaystyle \small \frac{10}{36}\ =\ \frac{5}{18}\)

Example Question #181 : Gmat Quantitative Reasoning

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:

\(\displaystyle \frac{21}{100}\)

\(\displaystyle \frac{4}{7}\)

\(\displaystyle \frac{3}{25}\)

\(\displaystyle \frac{9}{50}\)

Correct answer:

\(\displaystyle \frac{3}{25}\)

Explanation:

Since there are 300 people, \(\displaystyle 300\cdot .21=63\) people play baseball and \(\displaystyle 300\cdot .09=27\) of those people play both baseball and soccer. Therefore, there are \(\displaystyle 63-27=36\) people who play baseball but not soccer.

Probability: \(\displaystyle \frac{36}{300}=\frac{3}{25}\)

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:

\(\displaystyle \frac{1}{2}\)

\(\displaystyle \frac{2}{9}\)

\(\displaystyle \frac{17}{18}\)

\(\displaystyle \frac{4}{9}\)

\(\displaystyle \frac{2}{3}\)

Correct answer:

\(\displaystyle \frac{4}{9}\)

Explanation:

probability on one roll: \(\displaystyle \frac{4}{6}=\frac{2}{3}\)

for both times= \(\displaystyle \frac{2}{3}\times \frac{2}{3}= \frac{4}{9}\)

Example Question #1 : Data Interpretation

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:

\(\displaystyle \frac{1}{5525}\)

\(\displaystyle \frac{1}{140,608}\)

\(\displaystyle \frac{1}{64}\)

\(\displaystyle \frac{1}{2197}\)

Correct answer:

\(\displaystyle \frac{1}{5525}\)

Explanation:

The probability of drawing an ace first is \(\displaystyle \frac{4}{52}\) or \(\displaystyle \frac{1}{13}\).

Assuming an ace is the first card selected, the probability of selecting another ace is \(\displaystyle \frac{3}{51}\) or \(\displaystyle \frac{1}{17}\).

For the third card, the probability is \(\displaystyle \frac{2}{50}\) or \(\displaystyle \frac{1}{25}\).

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

\(\displaystyle \frac{1}{13}\times\frac{1}{17}\times\frac{1}{25}=\frac{1}{5525}\)

Example Question #2 : 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:

\(\displaystyle 16\)

\(\displaystyle 256\)

\(\displaystyle 32\)

\(\displaystyle 64\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 64\)

Explanation:

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 \(\displaystyle 2\cdot 4\cdot 4\cdot 2=64\) possibilities.

Example Question #2 : Data Interpretation

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

Possible Answers:

\(\displaystyle 0.333\)

\(\displaystyle 0.167\)

\(\displaystyle 0.5\)

\(\displaystyle 0.666\)

Correct answer:

\(\displaystyle 0.5\)

Explanation:

A standard dice has 6 faces numbered \(\displaystyle 1,2,3,4,5,6\).

 

There are \(\displaystyle 3\) even numbers, \(\displaystyle 2,4,6\), divided by the total number of faces:

\(\displaystyle \frac{3}{6}= 0.5\)

Example Question #193 : Gmat Quantitative Reasoning

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:

\(\displaystyle 0.192\)

\(\displaystyle 0.48\)

\(\displaystyle 0.352\)

\(\displaystyle 0.784\)

\(\displaystyle 0.8\)

Correct answer:

\(\displaystyle 0.352\)

Explanation:

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 \(\displaystyle 0.40 \cdot 0.40 = 0.16\)

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 \(\displaystyle 0.40 \cdot 0.60 \cdot 0.40 = 0.096\)

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

The probability of this happening is \(\displaystyle 0.60 \cdot 0.40 \cdot 0.40 = 0.096\)

Add these probabilities:

\(\displaystyle 0.096 + 0.096 + 0.16 = 0.352\)

Example Question #195 : Problem Solving Questions

Square

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:

\(\displaystyle 1\textrm{ to }1\)

\(\displaystyle 5\textrm{ to }2\)

\(\displaystyle 2\textrm{ to }1\)

\(\displaystyle 3\textrm{ to }1\)

\(\displaystyle 3\textrm{ to }2\)

Correct answer:

\(\displaystyle 1\textrm{ to }1\)

Explanation:

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 #5 : 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:

\(\displaystyle \$5.50\)

\(\displaystyle -\$4.50\)

\(\displaystyle \$0\)

\(\displaystyle \$4.50\)

\(\displaystyle -\$5.50\)

Correct answer:

\(\displaystyle -\$5.50\)

Explanation:

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

\(\displaystyle \frac{-\$5,500}{1,000} = -\$5.50\)

This is the expected value of one ticket. 

Example Question #3 : Data Interpretation

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:

\dpi{100} \small \frac{1}{5}\(\displaystyle \dpi{100} \small \frac{1}{5}\)

\(\displaystyle 1\)

\dpi{100} \small \frac{3}{5}\(\displaystyle \dpi{100} \small \frac{3}{5}\)

\dpi{100} \small \frac{4}{5}\(\displaystyle \dpi{100} \small \frac{4}{5}\)

\dpi{100} \small \frac{2}{5}\(\displaystyle \dpi{100} \small \frac{2}{5}\)

Correct answer:

\dpi{100} \small \frac{4}{5}\(\displaystyle \dpi{100} \small \frac{4}{5}\)

Explanation:

The easiest way to solve this is by using the complement. Only one of the five plates is NOT blue or green. So \dpi{100} \small \frac{1}{5}\(\displaystyle \dpi{100} \small \frac{1}{5}\) of the plates are NOT blue or green.  Therefore \dpi{100} \small 1-\frac{1}{5}=\frac{4}{5}\(\displaystyle \dpi{100} \small 1-\frac{1}{5}=\frac{4}{5}\) of the plates are blue or green.

Tired of practice problems?

Try live online GMAT prep today.

1-on-1 Tutoring
Live Online Class
1-on-1 + Class
Learning Tools by Varsity Tutors