GMAT Math : DSQ: Calculating discrete probability

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 Next →

Example Question #81 : Dsq: Calculating Discrete Probability

Some balls are placed in a large box; the balls include one ball marked "A", two balls marked "B", and so forth up to twenty-six balls marked "Z". A ball is drawn at random.

Given a particular letter of the alphabet, does the probability that that ball will be marked with that letter exceed $\frac{1}{70}$ ?

Statement 1: The letter appears in the word "Mississippi".

Statement 2: The letter does not appear in the word "carbide".

Possible Answers:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

The total number of balls in the box will be

1 + 2 + 3 + ... + 26 .

Since

$1+ 2 + 3 + ...+ N = \frac{N (N + 1)}{2}$ ,

it follows that the number of balls is

$1+ 2 + 3 + ...+ 26= \frac{26 (26 + 1)}{2} = \frac{26 \cdot 27}{2} = 351$ .

The number of balls with a given letter of the alphabet is equal to the number of its position in the alphabet; the probability of a ball with that letter being drawn is that number divided by the total number of balls, 351. Therefore, for this probability to exceed $\frac{1}{70}$ , we must have the relation

$\frac{M}{351} > \frac{1}{70}$

$\frac{M}{351} \cdot 351 > \frac{1}{70} \cdot 351$

$M > \frac{351}{70} = 5 \frac{1}{70}$ .

Therefore, M > 5 .

The 5th letter of the alphabet is "E", so in order to answer this question, it suffices to know whether the letter comes after "E" in the alphabet.

Either statement alone is sufficient to answer this question in the affirmative. Statement 1 establishes that the letter must be "I", "M", "P", or "S", all of which come after "E". Statement 2 establishes that the letter cannot be any of "A", "B", "C", "D", or "E", all five of which appear in the word "carbide".

Report an Error

Example Question #82 : Dsq: Calculating Discrete Probability

Some balls are placed in a large box; the balls include one ball marked "10", two balls marked "9", and so forth up to ten balls marked "1". A ball is drawn at random.

is an integer between 1 and 10 inclusive. True or false: the probability that the ball will have the number marked on it is greater than $\frac{1}{10}$ .

Statement 1: is a prime integer.

Statement 2: $N \le 5$

Possible Answers:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Explanation:

The total number of balls in the box will be

1 + 2 + 3 + ... + 10 .

Since

$1+ 2 + 3 + ...+ N = \frac{N (N + 1)}{2}$ ,

it follows that the number of balls is

$1+ 2 + 3 + ...+ 10= \frac{10 (10 + 1)}{2} = \frac{10 \cdot 11}{2} = 55$ .

The frequencies out of 55 of each outcome from 1 to 10, in order, are as follows:

$\left \{ 10, 9, 8, 7, 6, 5, 4, 3, 2, 1\right \}$

Their respective probabilities are their frequencies divided by 55:

$\left \{ \frac{10}{55}, \frac{9}{55}, \frac{8}{55}, \frac{7}{55}, \frac{6}{55}, \frac{5}{55}, \frac{4}{55}, \frac{3}{55}, \frac{2}{55}, \frac{1}{55} \right \}$ .

The probability that the ball will be marked "5" is

$\frac{6}{55} \approx 0.109 > 0.1 = \frac{1}{10}$ ;

therefore, the probability that the ball will be marked with any given integer less than or equal to 5 will be greater than $\frac{1}{10}$ .

The probability that the ball will be marked "6" is

$\frac{5}{55} \approx 0.091 < 0.1 = \frac{1}{10}$ ;

therefore, the probability that the ball will be marked with any given integer greater than or equal to 6 will be less than $\frac{1}{10}$ .

Therefore, it suffices to know whether the number on the ball is less than or equal to 5. Statement 2 states that the number on the ball is less than or equal to 5, so it is sufficient to answer the question in the affirmative. Statement 1 is insufficient, since there are primes less than or equal to 5 - 2, 3, and 5 - and one prime greater than 5, which is 7.

Report an Error

Example Question #83 : Dsq: Calculating Discrete Probability

Some balls are placed in a large box; the balls include one ball marked "10", two balls marked "9", and so forth up to ten balls marked "1". A ball is drawn at random.

is an integer between 1 and 10 inclusive. True or false: the probability that the ball will have the number marked on it is greater than $\frac{1}{10}$ .

Statement 1: is a perfect square integer.

Statement 2: $N \ge 5$

Possible Answers:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

The total number of balls in the box will be

1 + 2 + 3 + ... + 10 .

Since

$1+ 2 + 3 + ...+ N = \frac{N (N + 1)}{2}$ ,

it follows that the number of balls is

$1+ 2 + 3 + ...+ 10= \frac{10 (10 + 1)}{2} = \frac{10 \cdot 11}{2} = 55$ .

The frequencies out of 55 of each outcome from 1 to 10, in order, is as follows:

$\left \{ 10, 9, 8, 7, 6, 5, 4, 3, 2, 1\right \}$

Their respective probabilities are their frequencies divided by 55:

$\left \{ \frac{10}{55}, \frac{9}{55}, \frac{8}{55}, \frac{7}{55}, \frac{6}{55}, \frac{5}{55}, \frac{4}{55}, \frac{3}{55}, \frac{2}{55}, \frac{1}{55} \right \}$ .

The probability that the ball will be marked "5" is

$\frac{6}{55} \approx 0.109 > 0.1 = \frac{1}{10}$ ;

therefore, the probability that the ball will be marked with any given integer less than or equal to 5 will be greater than $\frac{1}{10}$ .

The probability that the ball will be marked "6" is

$\frac{5}{55} \approx 0.091 < 0.1 = \frac{1}{10}$ ;

therefore, the probability that the ball will be marked with any given integer greater than or equal to 6 will be less than $\frac{1}{10}$ .

Therefore, it suffices to know whether the number on the ball is less than or equal to 5.

Statement 1 alone is insufficient, since there are two perfect square integers from 1 to 5 (1 and 4) and one perfect square integer from 6 to 10 (9). Statement 2 alone is insufficient, since it is not clear whether the number on the ball is 5 or a number greater than 5. However, from the two statements together, it can be inferred that N = 9 , and that the probability of drawing a ball with this number is $\frac{2}{55} < \frac{1}{10}$ .

Report an Error

Example Question #84 : Dsq: Calculating Discrete Probability

A bag contains x red marbles, y blue marbles, and z green marbles. What is the probability of drawing a green marble?

(1) There's a probability of drawing a red marble.

(2) There's a probability of drawing a blue marble.

Possible Answers:

Statements (1) and (2) TOGETHER are NOT sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct answer:

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

Probability is a part to whole comparison.

With statement 1, we don't know nor can we determine the probability of drawing a green marble because we know nothing about the probability of drawing a blue marble. Therefore, statement 1 is not sufficient.

With statement 2, we don't know nor can we determine anything regarding the probability of drawing a red marble. Therefore, statement 2 is not sufficient.

However, taken together, we can determine that the probability of drawing a green marble is . Therefore, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Report an Error

Example Question #85 : Dsq: Calculating Discrete Probability

A coin is tossed n times. What is the probability of getting at least one tail?

(1) The probability of never flipping a head is $\frac{1}{8}$ .

(2) The probability of flipping at least one head is $\frac{7}{8}$ .

Possible Answers:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct answer:

EACH statement ALONE is sufficient.

Explanation:

Probability is the number of desired outcomes divided by the number of possible outcomes.

With statement 1, we are told the probability of never flipping a head is $\frac{1}{8}$ , which is the same as always flipping a tail. Since the probability of flipping a tail on a single flip is $\frac{1}{2}$ , we can determine the probability of flipping n tails is $\frac{1}{2}^{n}=\frac{1}{8}$ , which solves as $\frac{1}{2}^{3}=\frac{1}{8}$ . With n=3, we can solve for the probability of getting at least one tail is 1-probability of never getting a tail or 1-HHH:

$1-\frac{1}{8}=\frac{7}{8}$ .

Therefore, statement 1 alone is sufficient.

With statement 2, we are told the probability of flipping at least one head is $\frac{7}{8}$ . Since there are only 2 possible outcomes with each flip (heads or tails), the probability of flipping at least one head is the same as the probability of flipping at least one tail. Therefore, statement 2 alone is sufficient.

Therefore, the correct answer is EACH statement ALONE is sufficient.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 Next →

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Chicago, Algebra Tutors in Chicago, French Tutors in Denver, Chemistry Tutors in Miami, Computer Science Tutors in San Francisco-Bay Area, Algebra Tutors in Seattle, LSAT Tutors in Houston, Computer Science Tutors in Los Angeles, GRE Tutors in Miami, SAT Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Denver, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Chicago, ISEE Courses & Classes in Boston, ACT Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Denver, SSAT Test Prep in New York City, SSAT Test Prep in San Diego, GMAT Test Prep in Houston, ACT Test Prep in New York City, ISEE Test Prep in Dallas Fort Worth, SAT Test Prep in Miami, LSAT Test Prep in Philadelphia, SAT Test Prep in Washington DC, LSAT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : DSQ: Calculating discrete probability

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #81 : Dsq: Calculating Discrete Probability

Example Question #82 : Dsq: Calculating Discrete Probability

Example Question #83 : Dsq: Calculating Discrete Probability

Example Question #84 : Dsq: Calculating Discrete Probability

Example Question #85 : Dsq: Calculating Discrete Probability

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details