Work through the questions first, then open the answer key and explanations to check your work.
A community center surveyed 120 visitors about whether they attended a fitness class and whether they used the swimming pool during the same week. The results are shown in the table below.
| Used swimming pool | Did not use swimming pool | Total | |
|---|---|---|---|
| Attended fitness class | 28 | 32 | 60 |
| Did not attend fitness class | 18 | 42 | 60 |
| Total | 46 | 74 | 120 |
If one of the surveyed visitors is selected at random, what is the probability that the visitor used the swimming pool?
A number is selected at random from the set \(\{-8, -3, 4, 9, 12\}\). What is the probability that the selected number is a multiple of 4?
A parking lot contains 14 cars, and 5 of them are electric cars. If one car is selected at random from the parking lot, what is the probability that the car selected is electric?
At a community garden, 18 out of every 45 tomato plants produce yellow tomatoes. If one tomato plant is selected at random from the garden, what is the probability that it produces yellow tomatoes?
A box contains 18 mystery game cards. Of these cards, 7 are creature cards and 11 are spell cards. One card is selected at random from the box.
What is the probability that the selected card is a creature card? Enter your answer as a fraction or decimal, but not as a percent.
A community garden has 240 plants. Each plant is classified as a vegetable plant, a flower plant, or an herb plant. The probability that a randomly selected plant is a vegetable plant is \(0.35\), and the probability that a randomly selected plant is a flower plant is \(45\%\). How many of the plants are herb plants?
A community center recorded the types of classes attended during one week.
| Morning | Afternoon | Evening | Total | |
|---|---|---|---|---|
| Art | 18 | 12 | 10 | 40 |
| Fitness | 14 | 16 | 20 | 50 |
| Cooking | 8 | 6 | 16 | 30 |
| Total | 40 | 34 | 46 | 120 |
If one class attendance record is selected at random from the table, what is the probability that it is for a Fitness class? Express your answer as a fraction or decimal, but not as a percent.
A community theater sold 240 tickets for a weekend performance. Every ticket sold was either a student ticket, an adult ticket, or a senior ticket, and no ticket belonged to more than one category.
If a ticket is selected at random, the probability that it is a student ticket is \(\frac{3}{8}\), and the probability that it is an adult ticket is \(\frac{5}{12}\). How many senior tickets were sold?
A city transportation survey categorized 180 commuters by their primary travel method and work schedule.
| On-site Only | Hybrid | Fully Remote | Total | |
|---|---|---|---|---|
| Car | 42 | 18 | 10 | 70 |
| Bus | 24 | 16 | 8 | 48 |
| Bicycle | 14 | 20 | 6 | 40 |
| Train | 10 | 8 | 4 | 22 |
| Total | 90 | 62 | 28 | 180 |
If one commuter who works either a hybrid schedule or fully remote schedule is selected at random, what is the probability that the commuter primarily travels by bus or bicycle?
Enter your answer as a fraction or decimal.
A community center surveyed 108 members about the type of exercise class they attend most often and the time of day they usually attend. The results are shown in the table.
| Morning | Afternoon | Evening | Total | |
|---|---|---|---|---|
| Yoga | 14 | 10 | 8 | 32 |
| Cycling | 9 | 15 | 12 | 36 |
| Strength Training | 11 | 13 | 16 | 40 |
| Total | 34 | 38 | 36 | 108 |
If one member is selected at random from those who usually attend classes in the afternoon or evening, what is the probability that the member most often attends Cycling classes?
A community center surveyed members about which type of exercise class they attended during the past month. The results are shown in the table below.
| Morning Classes | Evening Classes | Total | |
|---|---|---|---|
| Yoga | 28 | 14 | 42 |
| Strength Training | 20 | 36 | 56 |
| Total | 48 | 50 | 98 |
If a surveyed member is known to have attended an evening class, what is the probability that the member attended yoga?
Enter your answer as a fraction or decimal, but not as a percent.
A media company stores files on two types of servers: archive servers and streaming servers. There are 9 archive servers, and each archive server contains 14 files larger than 2 gigabytes and 11 files that are not larger than 2 gigabytes. There are 7 streaming servers, and each streaming server contains 18 files larger than 2 gigabytes and 9 files that are not larger than 2 gigabytes.
If one file larger than 2 gigabytes is selected at random from all the files larger than 2 gigabytes on these servers, what is the probability that the selected file came from a streaming server?
\(\frac{46}{120}\)
The probability that a randomly selected visitor used the swimming pool is the total number of visitors who used the swimming pool divided by the total number of surveyed visitors.
From the table, 46 visitors used the swimming pool, and there were 120 visitors total. Therefore, the probability is \(\frac{46}{120}\).
Choice C is correct. The other choices use different visible totals from the table instead of the swimming-pool total.
\(\frac{3}{5}\)
The numbers in the set that are multiples of 4 are \(-8\), \(4\), and \(12\). There are 3 favorable outcomes out of 5 total numbers in the set, so the probability is \(\frac{3}{5}\).
\(\frac{5}{14}\)
Probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. There are 5 electric cars out of 14 total cars, so the probability is \(\frac{5}{14}\).
\(\frac{2}{5}\)
Probability is the number of favorable outcomes divided by the total number of outcomes. Since 18 out of every 45 plants produce yellow tomatoes, the probability is \(\frac{18}{45}\). Simplifying gives \(\frac{2}{5}\).
The probability of selecting a creature card is the number of creature cards divided by the total number of cards.
There are 7 creature cards and \(7+11=18\) total cards, so the probability is \(\frac{7}{18}\).
The fraction \(\frac{7}{18}\) is already in simplest form.
48
First find the number of vegetable plants: \(0.35 \times 240 = 84\).
Next find the number of flower plants: \(0.45 \times 240 = 108\).
Since every plant is in exactly one of the three categories, the number of herb plants is the total minus the other two categories:
\(240 - 84 - 108 = 48\).
Therefore, the correct answer is 48.
The total number of Fitness class records is 50, which is the row total for Fitness. The total number of class records is 120. Therefore, the probability is \(\frac{50}{120}\), which simplifies to \(\frac{5}{12}\).
The number of student tickets is \(240\times\frac{3}{8}=90\).
The number of adult tickets is \(240\times\frac{5}{12}=100\).
Since all 240 tickets are divided into the three categories, the number of senior tickets is \(240-90-100=50\).
The condition limits the sample space to commuters with either a hybrid schedule or a fully remote schedule.
First find the total number of commuters in that restricted group:
\(62+28=90\)
Next find how many of those commuters primarily travel by bus or bicycle.
Bus commuters in the restricted group: \(16+8=24\)
Bicycle commuters in the restricted group: \(20+6=26\)
Total favorable outcomes:
\(24+26=50\)
The conditional probability is therefore
\(\frac{50}{90}=\frac{5}{9}\)
So the correct answer is \(\frac{5}{9}\).
\(\frac{27}{74}\)
The condition is that the member usually attends in the afternoon or evening, so first restrict the sample space to those two columns.
The total number of members who attend in the afternoon or evening is \(38+36=74\).
The number of those members who most often attend Cycling classes is \(15+12=27\).
Therefore, the conditional probability is \(\frac{27}{74}\). Since 27 and 74 have no common factor greater than 1, the fraction is already simplified.
Because the question says the member is known to have attended an evening class, the sample space is limited to the 50 members in the Evening Classes column.
Of those 50 members, 14 attended yoga. Therefore, the conditional probability is \(\frac{14}{50}=\frac{7}{25}\), which is equivalent to \(0.28\).
\(\frac{1}{2}\)
First find the total number of files larger than 2 gigabytes on each type of server.
Archive servers: \(9 \times 14 = 126\) large files.
Streaming servers: \(7 \times 18 = 126\) large files.
The question asks for the probability that a selected large file came from a streaming server, given that the file is already known to be larger than 2 gigabytes. Therefore, the sample space includes only the large files.
Total large files: \(126 + 126 = 252\).
Probability = \(\frac{126}{252} = \frac{1}{2}\).
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