9.05 Experimental probability
A card is randomly selected and replaced from a normal deck of cards multiple times. The outcomes are shown in the given table:
Calculate the relative frequency of selecting:
A diamond.
A club.
A heart.
A spade.
A black card.
A red card.
| Suit Drawn | Frequency |
|---|---|
| \text{Diamond} | 15 |
| \text{Club} | 15 |
| \text{Heart} | 10 |
| \text{Spade} | 11 |
| \text{Total} | 51 |
The table shows the results of rolling a die multiple times:
How many times was the die rolled?
Find the relative frequency of not rolling a 3.
Find the experimental probability of rolling an even number.
| Outcome | Frequency |
|---|---|
| 1 | 13 |
| 2 | 12 |
| 3 | 20 |
| 4 | 14 |
| 5 | 15 |
| 6 | 16 |
The table shows 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 number and of rolling an odd number.
| Outcome | Frequency |
|---|---|
| 1 | 16 |
| 2 | 16 |
| 3 | 19 |
| 4 | 13 |
| 5 | 12 |
| 6 | 12 |
The table shows the outcomes of tossing three coins multiple times:
How many times were the three coins tossed?
Find the experimental probability of tossing:
3 tails.
At least 2 heads.
At least 1 tail.
Only 1 head.
Exactly 2 tails.
| Outcome | Frequency |
|---|---|
| \text{HHH} | 11 |
| \text{HHT} | 12 |
| \text{HTH} | 11 |
| \text{HTT} | 16 |
| \text{THH} | 12 |
| \text{THT} | 15 |
| \text{TTH} | 10 |
| \text{TTT} | 15 |
A die is rolled 60 times with the results recorded in the following table:
Find the experimental probability of:
Rolling a 6.
Rolling a 3 or greater.
Rolling a 3 or less.
| Number | Frequency |
|---|---|
| 1 | 10 |
| 2 | 12 |
| 3 | 8 |
| 4 | 10 |
| 5 | 8 |
| 6 | 12 |
A die is rolled 121 times with the results recorded in the following table:
Find the experimental probability of:
Rolling a 5.
Rolling a 4 or greater.
Rolling a 4 or less.
| Number | Frequency |
|---|---|
| 1 | 20 |
| 2 | 19 |
| 3 | 19 |
| 4 | 20 |
| 5 | 21 |
| 6 | 22 |
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 was the relative frequency of a lamb meal being ordered?
| Meal | Frequency |
|---|---|
| \text{Chicken} | 25 |
| \text{Beef} | 41 |
| \text{Lamb} | 44 |
| \text{Vegetarian} | 46 |
Boxes of toothpicks are examined and the number of toothpicks in each box is recorded in the following table:
If the number of toothpicks of another box were counted, find the experimental probability it will have:
89 toothpicks.
More than 90 toothpicks.
Less than 90 toothpicks.
| Number of toothpicks | Number of Boxes |
|---|---|
| 87 | 0 |
| 88 | 6 |
| 89 | 4 |
| 90 | 1 |
| 91 | 1 |
| 92 | 2 |
| 93 | 1 |
High school students attending an international conference were asked to register what language other than English they speak. The results are shown in the table:
How many students attended the conference?
Find the probability that a student chosen at random speaks:
French
Mandarin
Arabic or Spanish
Spanish or Other
| Language | Frequency |
|---|---|
| \text{French} | 20 |
| \text{Arabic} | 13 |
| \text{Spanish} | 21 |
| \text{Mandarin} | 19 |
| \text{Other} | 37 |
A coin was flipped 100 times with 51 tails recorded. What is the experimental
A coin was flipped 184 times with 93 heads recorded. Find the experimental probability of flipping heads with this coin.
On a production line, it was found that packaged foods contained trace amounts of nuts with relative frequency of 0.37. What percentage did not contain trace amounts of nuts?
Describe what would need to happen in an experiment for an event to obtain a relative frequency of 1.
The table shows the fighting style of each competitor in a mixed martial arts tournament:
Find the total number of competitors.
Find the relative frequency of a competitor using Karate.
Find the experimental probability of a competitor being a wrestler.
What is the most common fighting style?
Find the experimental probability of a competitor not being a Taekwondo fighter.
If 100 more competitors joined the competition, how many of them would you expect to use Karate as their fighting style?
| Event | Frequency |
|---|---|
| \text{Karate} | 40 |
| \text{Wrestling} | 54 |
| \text{Judo} | 47 |
| \text{Taekwondo} | 59 |
Each player draws as many dominoes as they like from a bag. A domino has two numbers from 1 to 6 on it as shown below. A high value domino occurs if the sum of its two numbers is greater or equal to 6. Otherwise it is a low value domino.
The table below shows how many dominoes each player has, and how many of them have a high value:
| Player | No. of dominoes drawn | No. of high value dominoes drawn |
|---|---|---|
| \text{Sam} | 5 | 5 |
| \text{Kristen} | 6 | 1 |
| \text{Aoife} | 7 | 6 |
| \text{Yan} | 5 | 4 |
A player wins by randomly selecting a low value domino from their drawn sample. Which player has the least chance of winning?
Three students were trying to determine the probability of every possible outcome when three coins are tossed. They tossed the coins and recorded the following results:
Find the relative frequency of getting 2 heads and a tail.
The students expect that if they toss the coins many more times, the probability of each outcome will become \dfrac{1}{4}.
Is this correct? Explain your answer.
| Outcome | Number of trials resulting in outcome |
|---|---|
| \text{A: } 3 \text{ heads} | 13 |
| \text{B: } 2 \text{ heads and a tail} | 34 |
| \text{C: } 2 \text{ tails and a head} | 40 |
| \text{D: } 3 \text{ tails} | 17 |
A retail store served 773 customers in October, and there were 44 complaints during that month.
Calculate the experimental probability that a customer complains. Give your answer as a percentage, rounded to the nearest whole percent.
At a set of traffic lights, the green light is on for 24 seconds, then the yellow light lasts for 3 seconds, and then the red light is on for 13 seconds. This cycle then repeats continuously.
If a car approaches the traffic light, calculate the probability that the light will be:
Green
Yellow
Red
Five schools compete in a basketball competition. The results from the last season are given in the table below:
| Schools competing each game | Winner |
|---|---|
| St Trinian's vs Ackley Bridge | St Trinian's |
| Ackley Bridge vs Summer Heights | Summer Heights |
| Lakehurst vs Marquess | Marquess |
| Marquess vs St Trinian's | St Trinian's |
| St Trinian's vs Summer Heights | Summer Heights |
| St Trinian's vs Lakehurst | Lakehurst |
| Ackley Bridge vs Marquess | Ackley Bridge |
| Marquess vs Summer Heights | Summer Heights |
| Lakehurst vs Summer Heights | Lakehurst |
| Ackley Bridge vs Lakehurst | Lakehurst |
Calculate the experimental probability that Ackley Bridge wins one of their matches.
An insurance company found that in the past year, of the 2558 claims made, and 1493 of them were from drivers under the age of 25. Calculate the experimental probability, to the nearest percentage, that a claim is filed by someone:
Under the age of 25.
25 years or older.
The table shows the number of trains that arrived on time at the local station during the week:
Calculate the experimental probability that a train will be on time on Monday, to the nearest percentage.
Find the greatest experimental probability of a train being on time.
Calculate the experimental probability of a train arriving on time across the entire week, to the nearest percentage.
| Day | Number of trains | On time |
|---|---|---|
| \text{Monday} | 29 | 22 |
| \text{Tuesday} | 24 | 23 |
| \text{Wednesday} | 21 | 19 |
| \text{Thursday} | 27 | 22 |
| \text{Friday} | 23 | 20 |
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.
The 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 least applications?
If the monthly applications are the same throughout the year, how many people will apply for UK over the next 12 months?
