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ACT Math : Data Analysis

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Example Question #52 : 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:

$\small 15.32\%$

$\small 21.94\%$

$\small 63.64\%$

$\small 59.34\%$

$\small 28.46\%$

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 $\small 28.46\%$ .

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

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:

$\small 0.19\%$

$\small 1.4\%$

$\small 2.35\%$

$\small 19.23\%$

$\small 0.14\%$

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 $\small 0.14\%$

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Example Question #51 : 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:

$\small 28.94\%$

$\small 40\%$

$\small 25\%$

$\small 27.78\%$

$\small 35\%$

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 $\small 25\%$

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Example Question #58 : How To Find The Probability Of An Outcome

$2\textup{ six-sided dice}$ 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:

$\small 41.67\%$

$\small 50\%$

$\small 13.89\%$

$\small 19.44\%$

$\small 16.67\%$

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 $\small 13.89\%$ .

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

$\textup{2 six-sided dice}$ 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:

$8.33\%$

$\small \small 11.11\%$

$\small 33.33\%$

$\small 27.88\%$

$\small 19.44\%$

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 $\small \small 11.11\%$ .

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Example Question #171 : Data Analysis

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:

$\frac{10}{31}$

$\frac{1}{3}$

$\frac{9}{31}$

$\frac{3}{31}$

$\frac{1}{2}$

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:

$\frac{10}{31}$

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Example Question #63 : How To Find The Probability Of An Outcome

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:

$\frac{4}{10}$

$\frac{7}{10}$

$\frac{1}{2}$

$\frac{2}{5}$

$\frac{3}{10}$

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:

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

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Example Question #64 : How To Find The Probability Of An Outcome

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:

$\frac{1}{2}$

$\frac{1}{7}$

$\frac{1}{6}$

$\frac{2}{7}$

$\frac{1}{5}$

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).
$\frac{1}{5}$

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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:

$\frac{3}{11}$

$\frac{11}{14}$

$\frac{2}{7}$

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

$\frac{1}{2}$

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:

$\frac{11}{14}$

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Example Question #62 : How To Find The Probability Of An Outcome

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:

$\frac{17}{20}$

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

$\frac{7}{20}$

$\frac{6}{20}$

$\frac{1}{5}$

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:

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

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ACT Math : Data Analysis

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #52 : How To Find The Probability Of An Outcome

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

Example Question #51 : How To Find The Probability Of An Outcome

Example Question #58 : How To Find The Probability Of An Outcome

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

Example Question #171 : Data Analysis

Example Question #63 : How To Find The Probability Of An Outcome

Example Question #64 : How To Find The Probability Of An Outcome

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

Example Question #62 : How To Find The Probability Of An Outcome

All ACT Math Resources

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