Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Data Analysis

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #54 : How To Find The Probability Of An Outcome

There are $\textup{35 tomatoes}$ , $\textup{55 onions}$ , and $\textup{33 pears}$ on a shelf. What is the probability of picking a tomato at random? Round to the nearest hundredth of a percent.

Possible Answers:

$\small 21.94\%$

$\small 28.46\%$

$\small 59.34\%$

$\small 15.32\%$

$\small 63.64\%$

Correct answer:

$\small 28.46\%$

Explanation:

For a probability question like this, first do a sum of the total possible outcomes. For the data given, this is $\small 35+55+33$ or $\small 123$ . Now, the probability of drawing a tomato is $\small \small \frac{35}{123}$ . Therefore, it is $\small 28.46\%$ .

Report an Error

Example Question #53 : Probability

A license plate is made up of four capital letters followed by three digits. If a plate is generated at random, what is the probability that it contains only vowels (A,E,I,O,U) for its letters? Presume that letters and numbers can repeat.

Possible Answers:

$\small 2.35\%$

$\small 0.14\%$

$\small 19.23\%$

$\small 1.4\%$

$\small 0.19\%$

Correct answer:

$\small 0.14\%$

Explanation:

Recall that you can calculate the probability of an event by dividing the number of desired outcomes by the total number of possible outcomes. First calculate the total possible outcomes. Think of your plate as having seven slots. The first four can have $\small 26$ possible outcomes. The last three can have $\small 10$ possible outcomes. (Remember, $\small 0$ is a number as well as $\small 1-9$ !)

Thus, you total outcome count is: 26*26*26*26*10*10*10 or 26^4 * 10^3

Now, for the vowel-only plates, you will have only choices for your letters. Therefore, you will have 5^4*10^3 . Thus, the probability is:

$\small \frac{5^4*10^3}{26^4*10^3}$ or $\small \small \frac{5^4}{26^4}$ , which is:

$\small 0.00136768670565$ or $\small 0.14\%$

Report an Error

Example Question #56 : How To Find The Probability Of An Outcome

What is the probability that a given random number between $\small \small 1000$ and $\small 9999$ is even and has a hundreds digit that is also even? Round to the nearest hundredth of a percent.

Possible Answers:

$\small 27.78\%$

$\small 28.94\%$

$\small 25\%$

$\small 40\%$

$\small 35\%$

Correct answer:

$\small 25\%$

Explanation:

This problem does not need to be as hard as it seems. You need to think of your number like a set of four slots.

Now, based on your description you know that the thousands digit can have $\small \small 1-9$ , as can the tens digit. The ones digit can only have $\small 0,2,4,6,8$ (since the number has to be even). Finally, the hundreds digit can only have $\small 0,2,4,6,8$ as well. Therefore, you can have a total of $\small \small 9*5*10*5$ or $\small 2250$ matching numbers. The total amount of numbers that you have are $\small 9000$ . This is because $\small 1000-1999$ represents a complete thousand, and so forth for the numbers up to $\small 9999$ . (You must be very careful when counting like this!)

Thus, your probability is $\small \small \frac{2250}{9000}$ or $\small 25\%$

Report an Error

Example Question #53 : Probability

$2\textup{ six-sided dice}$ are thrown. What is the probability that the sum of their sides will be $\small 8$ ? Round to the nearest hundredth of a percent.

Possible Answers:

$\small 50\%$

$\small 16.67\%$

$\small 13.89\%$

$\small 19.44\%$

$\small 41.67\%$

Correct answer:

$\small 13.89\%$

Explanation:

When two dice are thrown, remember that the total number of oucomes is $\small 6*6$ or $\small 36$ , NOT $\small 12$ . (Many students think that it is $\small 12$ .)

Now, for the data given, we know that the following pairs will work:

$\small 2,6$

$\small 3,5$

$\small 4,4$

$\small 5,3$

$\small 6,2$

Thus, there are $\small 5$ possible outcomes that will work for this data. This means that the probability of this outcome is $\small \frac{5}{36}$ or $\small 13.89\%$ .

Report an Error

Example Question #61 : Probability

$\textup{2 six-sided dice}$ are thrown. What is the probability that the product of their sides will be $\small \small 12$ ? Round to the nearest hundredth of a percent.

Possible Answers:

$\small 19.44\%$

$\small 27.88\%$

$8.33\%$

$\small 33.33\%$

$\small \small 11.11\%$

Correct answer:

$\small \small 11.11\%$

Explanation:

When two dice are thrown, remember that the total number of oucomes is $\small 6*6$ or $\small 36$ , NOT $\small 12$ . (Many students think that it is $\small 12$ .)

Now, for the data given, we know that the following pairs will work:

$\small 2,6$

$\small \small 3,4$

$\small 4,3$

$\small 6,2$

Thus, there are $\small \small 4$ possible outcomes that will work for this data. This means that the probability of this outcome is $\small \small \frac{4}{36}$ or $\small \small 11.11\%$ .

Report an Error

Example Question #61 : Probability

If a person is born in the month of January, what is the probability they are born on a day that is divisible by ? Give your answer as a reduced fraction.

Possible Answers:

$\frac{1}{2}$

$\frac{10}{31}$

$\frac{3}{31}$

$\frac{1}{3}$

$\frac{9}{31}$

Correct answer:

$\frac{10}{31}$

Explanation:

To find the probability, divide the number of outcomes that fit the event description by the total possible number of outcomes. There are 31 days in January, so that is our denominator. Of those, 3,6,9,12,15,18,21,24,27,30 are divisble by three, which is 10 of the days. Thus the answer is:

$\frac{10}{31}$

Report an Error

Example Question #61 : Probability

There is a $10\textup{-sided}$ fair die, what is the probability that you roll a prime number when rolling it once? (Leave your answer as a reduced fraction.)

Possible Answers:

$\frac{4}{10}$

$\frac{3}{10}$

$\frac{1}{2}$

$\frac{2}{5}$

$\frac{7}{10}$

Correct answer:

$\frac{2}{5}$

Explanation:

The total number of outcomes that fit the event (rolling a prime number) are the number of primes below 10: 2, 3, 5, 7 for a total of 4.
divide that but the total number of outcomes (10) and reduce:

$\frac{4}{10}= \frac{2}{5}$

Report an Error

Example Question #63 : Probability

You are trying to guess your friend's favorite day of the week. You know it's not a day that begins with "t". What is the chance that you guess correctly on your first try? Leave your answer as a simplified fraction.

Possible Answers:

$\frac{1}{6}$

$\frac{1}{7}$

$\frac{1}{5}$

$\frac{2}{7}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{5}$

Explanation:

There are 2 days that begin with "t". We know those cannot be the days. Since you are guessing you can only guess 1 outcome. The chance that that day is the corect one is the number of ways you can get it right (1, by guessing it right the first time) divide by the total number of outcomes (5).
$\frac{1}{5}$

Report an Error

Example Question #61 : How To Find The Probability Of An Outcome

There is an urn with three red balls, four green balls, and seven white balls in it. If you draw out a single ball, what is the probability that you don't pull out a red ball?

Possible Answers:

$\frac{11}{14}$

$\frac{3}{14}{}$

$\frac{2}{7}$

$\frac{3}{11}$

$\frac{1}{2}$

Correct answer:

$\frac{11}{14}$

Explanation:

To find the probability of an event, divide the number of ways the event can happen by the total number of outcomes.

There are 11 balls that are not red, so there are 11 ways there can be a not red ball picked.

There are 14 balls total in the urn so the probability we pick a not red ball is:

$\frac{11}{14}$

Report an Error

Example Question #62 : Probability

You are rolling a 20 sided die. What is the probability that you roll a multiple of 6 when rolling the die? Simplify any fractions in your answer.

Possible Answers:

$\frac{1}{5}$

$\frac{7}{20}$

$\frac{17}{20}$

$\frac{3}{20}{}$

$\frac{6}{20}$

Correct answer:

$\frac{3}{20}{}$

Explanation:

Divide the total number of ways to get the desire event by the total number of outcomes.

Since it is a 20 sided die there are 20 outcomes possible, but only 6, 12, and 18 are divisible by 6.

Thus, the probability that you roll a number divisible by 6 is:

$\frac{3}{20}{}$

Report an Error

View ACT Math Tutors

Kaitlyn
Certified Tutor

Fairfield University, Bachelor of Science, Biology, General. NUI Galway Ireland, Master of Science, Neuroscience.

View ACT Math Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

View ACT Math Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, Spanish Courses & Classes in Denver, GMAT Courses & Classes in New York City, Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Philadelphia, SSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Los Angeles, SSAT Courses & Classes in Denver, Spanish Courses & Classes in Boston, GRE Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Seattle, SAT Test Prep in Phoenix, SAT Test Prep in Houston, LSAT Test Prep in Seattle, ACT Test Prep in Washington DC, MCAT Test Prep in Phoenix, GRE Test Prep in Philadelphia, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Chicago, ISEE Test Prep in Phoenix

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ACT Math : Data Analysis

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #54 : How To Find The Probability Of An Outcome

Example Question #53 : Probability

Example Question #56 : How To Find The Probability Of An Outcome

Example Question #53 : Probability

Example Question #61 : Probability

Example Question #61 : Probability

Example Question #61 : Probability

Example Question #63 : Probability

Example Question #61 : How To Find The Probability Of An Outcome

Example Question #62 : Probability

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: