8.01 Experimental probability
If the relative frequency of an event is 1, the event:
Happened for most of the trials.
Didn’t happen.
Happened on each trial.
A bag contains 24 red marbles and 26 blue marbles.
What is the probability of drawing a red marble?
A bag contains 28 red marbles, 29 blue marbles, and 27 black marbles.
What is the probability of drawing a blue marble?
A single trial is drawing a marble from the bag, writing down the colour, and putting it back. If this trial is repeated 400 times, how many blue marbles should you expect? Round your answer to the nearest whole number.
Mohamad watched cars drive past his house over five minutes. In this time, 12 cars went by, and 10 of those cars were white. What is the experimental probability of a car being coloured white?
Ryan decided to flip a coin 20 times.
How many times would he expect a head to appear?
After he finished flipping the coins, he noticed that heads had appeared 11 times. Write the experimental probability of getting a head.
Rosey has a bag with 2 red balls, 2 blue balls, and 2 green balls in it. She took a ball out of the bag and returned it 36 times.
How many times would she expect to get a red ball?
After she finished, she noticed that she had drew a red ball 15 times. Write the experimental probability of getting a red ball as a fraction.
A retail store served 989 customers in October, and there were 21 complaints during that month. What is the experimental probability that a customer complains? Round your answer to the nearest whole percent.
An insurance company found that in the past year, of the 2523 claims made, 1492 of them were from drivers under the age of 25.
Find the experimental probability that a claim is filed by someone under the age of 25. Round your answer to the nearest whole percent.
Find the experimental probability that a claim is filed by someone 25 or older. Round your answer to the nearest whole percent.
Five schools compete in a basketball competition. The results from the last season are given in the table below:
| Match | Winner | Match | Winner | |
|---|---|---|---|---|
| Lakehurst v St Trinian's | Lakehurst | St Trinian's v Ackley Bridge | St Trinian's | |
| Summer Heights v Marquess | Marquess | Marquess v Lakehurst | Lakehurst | |
| Lakehurst v Ackley Bridge | Ackley Bridge | Lakehurst v Summer Heights | Summer Heights | |
| St Trinian's v Marquess | Marquess | Marquess v Ackley Bridge | Ackley Bridge | |
| Summer Heights v Ackley Bridge | Ackley Bridge | St Trinian's v Summer Heights | St Trinian's |
What is the experimental probability that Ackley Bridge wins a match?
At the main traffic light in town going north to south, the green light is on for 27 seconds, then the yellow light lasts for 3 seconds, and then the red light is on for 10 seconds. This cycle then repeats.
If a car approaches the traffic light, what is the probability that the light will be:
Green?
Yellow?
Red?
Beth is testing a coin to see if it is fair. She has flipped the coin 100 times and recorded 52 tails.
What is the experimental probability of flipping tails with this coin? Write your answer in decimal form.
Beth now wants to tell the coin manufacturer about the fairness of the coin. What should she tell them?
Beth tested the coin again. This time she flipped the coin 1000 times, and flipped 504 tails. What is the experimental probability of flipping tails based on this second experiment? Write your answer in decimal form.
Given the two experiments, can Beth say the coin is fair? Explain your answer?
The experimental probability that a commuter uses public transport is 30\%. Out of 200 commuters, how many would you expect to use public transport?
If the probability of an event is \dfrac{3}{4}, how many times would you expect it to occur in 76 trials?
A medical student is predicting how many people in their town will have certain genes. The population of their town is 1\,600\,000.
The probability of a person having the gene for red hair is 3\%. How many people in the town are expected to have this gene?
The probability of a person having the gene for tetrachromacy is 0.03\%. How many people in the town are expected to have this gene?
A factory produces tablet computers. In March, it produced 7000 tablets, and 140 were found to be faulty.
What is the experimental probability that a tablet produced by the factory is faulty?
The factory plans to produce 8000 tablets in April. How many should they expect to be faulty?
To prepare for the week ahead, a restaurant keeps a record of the number of each main meal ordered throughout the previous week:
How many meals were ordered altogether?
What is the experimental probability that a customer will order a chicken meal? Round your answer to the nearest whole percent.
| Meal | Frequency |
|---|---|
| \text{Chicken} | 21 |
| \text{Beef} | 55 |
| \text{Lamb} | 55 |
| \text{Vegetarian} | 31 |
The table tabulates the results of rolling a die multiple times:
Find the experimental probability of not rolling a number less than 3.
Find the relative frequency of not rolling a prime number.
Find the sum of the relative frequencies of rolling a 1, 2, 3, 4, 5 and 6.
Find the sum of the experimental probabilities of rolling an even or odd number.
| Outcome | Frequency |
|---|---|
| 1 | 17 |
| 2 | 14 |
| 3 | 12 |
| 4 | 13 |
| 5 | 12 |
| 6 | 16 |
Boxes of matchsticks are examined and the number of matchsticks in each box is recorded in the table:
If the number of matchsticks of another box were counted, what is the experimental probability it will:
Have 89 matchsticks?
Have more than 90 matchsticks?
Have less than 90 matchsticks?
| Number of matchsticks | Number of Boxes |
|---|---|
| 87 | 0 |
| 88 | 0 |
| 89 | 7 |
| 90 | 5 |
| 91 | 6 |
| 92 | 5 |
| 93 | 3 |
The following frequency table shows the number of people that came to donate blood and their respective weights:
If this group is considered to be representative of the population, what is the probability that someone in the population weighs 50 to 54 \text{ kg}?
What is the probability that someone weighed between 60 and 69 \text{ kg} inclusive?
| \text{Weight in kg } (x) | \text{Frequency } (f) |
|---|---|
| 40-44 | 4 |
| 45-49 | 1 |
| 50-54 | 1 |
| 55-59 | 3 |
| 60-64 | 10 |
| 65-69 | 8 |
| 70-74 | 2 |
| \text{Total} | 29 |
A die is rolled 60 times and the results are recorded in the following table:
Using this frequency table, find the experimental probability of rolling a:
6
3 or higher
3 or lower
| Number | Frequency |
|---|---|
| 1 | 11 |
| 2 | 12 |
| 3 | 12 |
| 4 | 12 |
| 5 | 11 |
| 6 | 2 |
The table tabulates the outcomes of tossing three coins multiple times:
How many times was the experiment repeated?
Find the experimental probability of tossing:
3 tails
at least 2 heads
at least 1 tail
only 1 head
| Outcome | Frequency |
|---|---|
| \text{HHH} | 13 |
| \text{HHT} | 13 |
| \text{HTH} | 14 |
| \text{HTT} | 11 |
| \text{THH} | 13 |
| \text{THT} | 14 |
| \text{TTH} | 11 |
| \text{TTT} | 13 |
A mixed martial arts club posted the results from the tournaments last year. The table shows the main fighting style of the winner for each tournament:
What was the total number of tournaments?
What is the experimental probability of a wrestler winning?
Which is the most successful fighting style?
If 1000 further tournaments are to be held, how many tournaments would you expect Judo fighters to win?
| Event | Frequency |
|---|---|
| \text{Karate} | 40 |
| \text{Wrestling} | 55 |
| \text{Judo} | 46 |
| \text{Taekwondo} | 59 |
The following table shows the number of trains that arrived on time at the local station during the week:
What is the experimental probability that a train will be on time on Monday? Round your answer to the nearest whole percent.
What was the highest experimental probability of a train being on time out of each of the five days? Round your answer to the nearest whole percent.
What is the experimental probability of a train arriving on time across the entire week? Round your answer to the nearest whole percent.
| Day | Number of trains | On time |
|---|---|---|
| \text{Monday} | 29 | 22 |
| \text{Tuesday} | 21 | 18 |
| \text{Wednesday} | 28 | 26 |
| \text{Thursday} | 26 | 20 |
| \text{Friday} | 23 | 19 |
Maria is tossing a coin. She keeps tossing the coin until a Tail appears. Her first set of tosses went Heads, Heads, Tails. So she stopped after three tosses. She repeated the experiment 19 more times and recorded her results in the following table:
Based off Maria's experiment, what is the experimental probability that it takes 5 tosses of the coin before a Tail appears?
Theoretically, what is the probability that it takes 5 tosses of a coin before a Tail appears?
Was the experimental probability Maria found equal, greater or less than the theoretical probability?
| Number of Tosses before a Tail appears | Frequency |
|---|---|
| 1 | 7 |
| 2 | 3 |
| 3 | 4 |
| 4 | 3 |
| 5 | 3 |
Homer used a spinner to choose "YES" or "NO". The table shows three different days, how many times he spun the spinner and how many times it landed on "YES":
| Day | Number of spins | Number of "YES"s |
|---|---|---|
| 1 | 6 | 3 |
| 2 | 30 | 9 |
| 3 | 84 | 20 |
Yvonne wants to reuse the spinner that Homer used. Which spinner should she pick?
Consider the table showing the status of a domino game being played by four players:
Each player draws as many dominos as they like from a bag. A domino has two numbers from 1 to 6. A high value domino occurs if the sum of its two numbers is greater or equal to 6 while a low value domino occurs otherwise.
A player wins by randomly selecting a low value domino from their drawn sample. At this point in the game, which player has the lowest chance of winning?
| Player | Number of dominoes drawn | Number of high valued dominoes |
|---|---|---|
| A | 10 | 9 |
| B | 7 | 1 |
| C | 8 | 7 |
| D | 6 | 4 |
Consider the column graph showing outcomes of a coin toss experiment:
How many times was the coin flipped?
What was the relative frequency of heads in this experiment?
The column graph shows the four countries that university students applied to for exchange in the last month:
What is the relative frequency of the country with the fewest applications?
If the monthly applications are the same throughout the year, how many people in total will apply for UK over the next six months?
The size of several earthquakes was measured over a period of time and the results are presented in the histogram below:
Estimate the probability that an earthquake will measure 5, 6, or 7.
Estimate the probability that an earthquake measures less than 5.
This histogram shows the number of people that waited in line for a rollercoaster at a theme park, and the length of time they had to wait:
Find the probability that someone waited in line for under 40 minutes.
Find the probability that someone had to wait at least 50 minutes to be served.
The following histogram shows the heights of people that were surveyed at a particular rollercoaster ride in a theme park:
Estimate the probability that someone randomly chosen at the park was between 130 and 150 \text{ cm} tall.
Find the probability that someone randomly chosen was at most 130 \text{ cm} tall.
