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ACT Math : Probability

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Example Questions

Example Question #164 : Data Analysis

In a particular high school, 200 students are freshmen, 150 students are sophomores, 250 students are juniors, and 100 students are seniors. Twenty percent of freshmen are in honors classes, ten percent of sophomores are in honors classes, twelve percent of juniors are in honors classes, and thirty percent of seniors are in honors classes.

If a student is chosen at random, what is the probability that that student will be a student who attends honors classes?

Possible Answers:

$\frac{5}{7}$

$\frac{9}{50}$

$\frac{9}{100}$

$\frac{23}{70}$

$\frac{23}{140}$

Correct answer:

$\frac{23}{140}$

Explanation:

First calculate the number of students:

200+150+250+100=700

The probability of drawing an honors student will then be the total number of honors students divided by the total number of students attending the school:

$\frac{200(.20)+(150)(.10)+(250)(.12)+(100)(0.30)}{700}$

$\frac{115}{700}=\frac{23}{140}$

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Example Question #61 : Discrete Probability

If a student is chosen at random, what is the probability that that student will be a senior student and a student who does not attend honors classes?

Possible Answers:

$\frac{3}{10}$

$\frac{4}{35}$

$\frac{2}{5}$

$\frac{3}{70}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{10}$

Explanation:

First calculate the number of students:

200+150+250+100=700

The percentage of seniors that do not attend honors classes is:

(1-.30)=.70

Therefore, the probability of selecting a student who is a senior and one who does not attend honors classes is:

$\frac{100}{700}(.70)=\frac{1}{10}$

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Example Question #51 : Probability

There are 4 blue marbles, 5 green marbles, 7 black marbles, and 3 white marbles in a jar. If you reach in and grab out one marble, what is the probabilty of drawing a green marble?

Possible Answers:

$\frac{5}{19}$

$\frac{14}{19}$

$\frac{1}{5}$

$\frac{5}{16}$

$\frac{4}{19}$

Correct answer:

$\frac{5}{19}$

Explanation:

To calculate the probability of an event happening, take the number of ways to draw a green marble (5, because there are 5 possible green marbles to choose) by the total number of ways to draw a marble from the jar (19). Thus the answer is $\frac{5}{19}$

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Example Question #52 : Probability

A fair, six sided die is number with the numbers one through three with each number appearing twice. What is the chance that you roll a two when rolling the die one time?

Possible Answers:

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{3}$

Explanation:

To calculate a probability, divide the possible ways to get the desire outcome by the total possible number of outcomes. We only care about rolling a 2, which can happen in 2 different ways (because there are two 2s on the die).

Thus we get:

$\frac{2}{6}=\frac{2\cdot 1}{2\cdot 3}=\frac{1}{3}$

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Example Question #53 : Probability

When rolling $\textup{2 fair dice}$ , what is the probability that the sum of their faces will be ? Reduce all fractions.

Possible Answers:

$\frac{1}{6}$

$\frac{1}{7}$

$\frac{1}{36}$

$\frac{7}{6}$

$\frac{7}{36}$

Correct answer:

$\frac{1}{6}$

Explanation:

To find the probability that two dice sum to seven we need to figure out the total number of ways that can happen. Represent the rolls as an ordered pair, with the first number in the pair corresponding to the first roll, and the second to the second roll. Then all the ways to get a sum of 7 are as follows:

(1,6),(2,5),(3,4),(4,3),(5,2),(6,1) - or 6 different ways.

There are 6*6 = 36 possible outcomes when rolling two dice (6 different ways the first roll could come out, and 6 ways the second roll could come out)
thus the probability the sum is 7 is:

$\frac{6}{36}=\frac{1}{6}$

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Example Question #53 : How To Find The Probability Of An Outcome

There are $14\textup{ cups}$ , $\textup{33 dishes}$ , and $\textup{41 spoons}$ in a box. What is the chance of someone drawing out a dish then a spoon, presuming that he or she does not place items back into the box after drawing them out? Round to the nearest hundredth of a percent.

Possible Answers:

$\small \small 47.13\%$

$\small 17.67\%$

$\small 18.04\%$

$\small 17.47\%$

$\small 16.33\%$

Correct answer:

$\small 17.67\%$

Explanation:

For a probability question like this, first do a sum of the total possible outcomes. For the data given, this is $\small 14+33+41$ or $\small 88$ . Now, the probability of drawing a dish is $\small \frac{33}{88}$ . After this, there are $\small 87$ items in the box. The probability of drawing a spoon after this is $\small \small \frac{41}{87}$ .

Now, when two events are sequential like this, the probability of the two together is calculated by multiplying their respective probabilities. Thus, your total probability is $\small \small \frac{33}{88} * \frac{41}{87} = \frac{1353}{7656}$ or $\small 17.67\%$

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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 $\small 28.46\%$ .

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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 $\small 0.14\%$

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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 $\small 25\%$

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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 $\small 13.89\%$ .

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ACT Math : Probability

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #164 : Data Analysis

Example Question #61 : Discrete Probability

Example Question #51 : Probability

Example Question #52 : Probability

Example Question #53 : Probability

Example Question #53 : How To Find The Probability Of An Outcome

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

All ACT Math Resources

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