In an experiment, several balls coloured either green or black and numbered 1 to 11 are placed in a bag. The table shows all the outcomes that occured:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Green | × | × | × | × | × | × | × | × | × | × | × |
| Black | × | × | × | × | × | × |
Find the probability that a ball drawn at random:
Is black.
Has the number 2.
Has the number 7.
Has a number 3 or higher.
Is green and has the number 5.
Is green or has the number 5.
At a factory, 1000 computers were tested with 15 found to be faulty. Calculate the experimental probability that a computer at this factory will be faulty.
A die is rolled 60 times and the results are recorded in the table:
Calculate the relative frequency of rolling a 6.
Calculate the relative frequency of rolling a 3 or higher.
Calculate the relative frequency of rolling a 3 or lower.
| Number | Frequency |
|---|---|
| 1 | 8 |
| 2 | 10 |
| 3 | 8 |
| 4 | 10 |
| 5 | 10 |
| 6 | 14 |
A bag contains four times as many yellow marbles as blue marbles.
If a marble is chosen at random, find the probability that it is yellow.
Hence find the probability of a blue marble being chosen.
At a golf course, the number of golf balls lost each day over several days were recorded, and rounded to the nearest 10. The table shows the results:
Using the data, estimate the probability that more than 39 golf balls will be lost tomorrow.
| Golf Balls Lost | Days |
|---|---|
| 10 | 5 |
| 20 | 5 |
| 30 | 1 |
| 40 | 4 |
| 50 | 3 |
A group of students were surveyed on their eye colour. The results are shown in the table:
Calculate the percentage of students that had hazel eyes.
Calculate the least number of students that could have completed the survey.
| Brown | Blue | Green | Hazel |
|---|---|---|---|
| 70\% | 15\% | 2\% |
The following table shows the number of people who scored a certain mark on a recent test. The test is marked out of 50.
Calculate the probability that someone scored more than 50\% on the test.
Calculate the probability that someone scored between 21 and 40 inclusive.
| Marks % | Frequency |
|---|---|
| 11-15 | 5 |
| 16-20 | 1 |
| 21-25 | 6 |
| 26-30 | 2 |
| 31-35 | 4 |
| 36-40 | 9 |
| 41-45 | 10 |
| 46-50 | 3 |
| \text{Total} | 40 |
The following table shows the weekly wage of a number of workers that were surveyed:
Calculate the probability that a worker chosen from the sample has a wage of at least \$280 per week.
Calculate the probability that a worker chosen from the sample has a wage of more than \$294.
| Weekly wages in dollars | Frequency |
|---|---|
| 220-234 | 5 |
| 235-249 | 3 |
| 250-264 | 2 |
| 265-279 | 2 |
| 280-294 | 10 |
| 295-309 | 2 |
| 310-324 | 2 |
| \text{Total} | 26 |
The graph shows the four countries that university students applied to for exchange in the last month. Calculate the relative frequency of the country with the fewest applications.
The following graph shows the number of people that were served at a furniture store, and the length of time it took to serve them:
Calculate the probability that someone was served in under 40 minutes.
Calculate the probability that someone had to wait at least 50 minutes to be served.
The size of several earthquakes was measured over a period of time and the results are presented in the graph. The numbers on the horizontal axis represent the class centres:
Calculate the probability that an earthquake will measure 5, 6, or 7.
Calculate the probability that an earthquake measures less than 5.
Of 50 people buying coffee at a cafe, 39 bought a latte.
Calculate the fraction of people that bought a latte.
In one day, the cafe had 550 customers. How many would you expect to order a latte?
The table shows the main fighting style of each fighter in a mixed martial arts tournament:
Calculate the total number of fighters.
Calculate the relative frequency of a fighter using Karate.
Calculate the experimental probability of a fighter using wrestling.
Calculate the probablity that a fighter does Judo.
| Style | Frequency |
|---|---|
| \text{Karate} | 40 |
| \text{Wrestling} | 54 |
| \text{Judo} | 47 |
| \text{Taekwondo} | 59 |
Calculate the experimental probability of a Taekwondo fighter competing.
Which is the most common fighting style?
If 100 further tournaments were to be held, which fighting style would you expect to be the least used?
A maternity ward delivers the following number of babies each day for two weeks:
5, 6, 4, 7, 6, 6, 4, 6, 5, 5, 6, 5, 6, 6
How many babies can you expect the ward to deliver on any particular day?
How many babies would you expect the ward to deliver in a year?
Boxes of individually wrapped chocolates, with 20 chocolates per box, are randomly sampled to see how many blueberry chocolates are in each box.
The results from the samples are shown in the table:
| Box No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Blueberry bites | 0 | 1 | 2 | 1 | 2 | 3 | 3 | 0 | 3 | 4 |
How many samples were taken?
Calculate the fraction of blueberry chocolates in box 2.
How many blue berry chocolates would you expect to be in each box?
Of 3000 students graduating as teachers from a particular university, 8\% graduate as Mathematics teachers.
How many students graduated as Mathematics teachers from this university?
In the country, there are 6900 new graduate teachers. How many are likely to be Mathematics teachers?