A spinner is divided equally into 5 sections, with 2 sections coloured white.
Find the probability of landing on white.
If the spinner is spun 685 times, how many times would you expect it to land on white?
A fair die is rolled 18 times.
Find the probability of getting a 1 on a single roll of a die.
How many times would you expect a 1 to come up in the 18 rolls?
260 fair dice are rolled.
Calculate the probability of getting an even number on a single roll of a die.
How many times would you expect an even number to come up on the 260 dice?
If Maria rolls a die 48 times, how many twos would she expect to come up?
If Buzz flips a coin 96 times, how many tails would he expect to come up?
Valerie flips 3 coins at once and repeats this 40 times.
For each time that Valerie flips 3 coins at once, find the probability that all 3 coins show heads.
Hence find the probability that at least 1 of the coins shows tails.
How many times can she expect 3 heads to come up at once in the 40 trials?
How many times can she expect at least 1 tail to come up in the 40 trials?
Dave rolls 2 dice at once and repeats this 36 times.
How many times can he expect the number 3 to appear in total?
How many times in total can he expect an even number to appear on a die?
40 people are given Drug X for the treatment of a disease. Drug X has a success rate of 30 \%. What is the predicted number of participants who will be treated successfully?
The given table presents the results of multiple coin tosses with a biased coin:
| Heads | Tails | |
|---|---|---|
| Frequency | 62 | 38 |
How many times was the coin tossed?
Find the experimental probability of tossing a head.
Find the experimental probability of tossing a tail.
If this coin was tossed 600 times, how many times would you expect it to land on a head?
If this coin was tossed 800 times, how many times would you expect it to land on a tail?
A biased coin is tossed 100 times and the results are presented in the table below. How many times would you expect the coin to land on a tail if the coin was tossed:
400 times?
500 times?
600 times?
920 times?
| Heads | Tails | |
|---|---|---|
| Frequency | 44 | 56 |
A card is selected at random, the result is recorded and the card is placed back in the deck. This is repeated multiple times. Consider the two tables below. In which table are the results closest to the expected outcome?
| Color | Frequency |
|---|---|
| \text{Black} | 54 |
| \text{Red} | 55 |
| Suit | Frequency |
|---|---|
| \text{Spade} | 21 |
| \text{Heart} | 34 |
| \text{Diamond} | 21 |
| \text{Club} | 33 |
If the probability of an event occurring is \dfrac{11}{25}, how many times would you expect the event to occur in 575 trials?
Amelia selects a card 260 times from a standard deck of 52 cards, with replacement.
How many diamonds can she expect to draw?
How many black cards can she expect to draw?
How many royal cards (Kings, Queens and Jacks) can she expect to draw?
How many times can she expect to draw the King of diamonds?
1000 transistors were tested at a factory, and 12 were found to be faulty.
Find the experimental probability that a transistor at this factory will be faulty.
If another 5000 transistors were tested, how many of these would you expect to be faulty?
Sally enters a raffle every week and each of these weeks, 130 tickets are sold. Find the number of times she can expect to win in a half-year period if she purchases:
1 ticket every week.
10 tickets every week.
A car manufacturer found that 1 in every 4 cars they were producing had faulty brake systems. If they had already sold 5060 cars, how many of those already sold would they expected will need to be repaired?
A bag contains 29 yellow marbles, 21 blue marbles and 10 pink marbles. If a marble is randomly selected from the bag 300 times with replacement, how many times you would expect to pick a marble that is:
Yellow?
Blue?
Pink?
Yellow or pink?
Blue or pink?
Yellow, blue or pink?
The probability of a person developing Valcyxin's Disease is 0.08\%. If there are 1\,600\,000 people in the population, how many of them are expected to develop the disease?
Sixteen fair dice were rolled and a 2 occurred on four of the dice.
What was the relative frequency of rolling a 2?
Is your answer to part (a) the same as the theoretical probability of rolling a 2? Explain your answer.
How many times would you expect a 2 to occur if 48 dice are rolled, using the experimental probability?
How many times would you expect a 2 to occur if 48 dice are rolled, using the theoretical probability?
Why doesn't the experimental probability match the theoretical probability?
Random selections were made from a set of cards labelled from 1 to 7. The following table shows the results:
How many selections were made in total?
Find the experimental probability of drawing a 3.
Find the experimental probability of not drawing an odd number.
Find the relative frequency of drawing a number greater than 4.
If 1000 random selections were made, how many times would you expect to draw a number divisible by 5?
| Outcome | Frequency |
|---|---|
| 1 | 55 |
| 2 | 61 |
| 3 | 59 |
| 4 | 64 |
| 5 | 63 |
| 6 | 61 |
| 7 | 55 |
In the lead-up to an election, a group of people were asked which candidate they will vote for. The following table summarizes the results of the survey:
How many people were surveyed?
According to these results, if 4\,576\,100 voters are expected to vote in the next election, how many of those votes would be for Candidate C?
| Candidate | Number of people |
|---|---|
| \text{A} | 79 |
| \text{B} | 96 |
| \text{C} | 93 |
Police want to determine where along a stretch of road to install a speed camera. Over a period of time, they measured the number of car accidents at each point along the road, and positioned the speed camera at the point where car accidents are most likely.
Apart from speed, state whether these factors might contribute to a higher incidence of car accidents at a particular spot:
Signs on the road indicating the speed limit.
Mechanical problems with cars.
Poor lighting on the road.
The steep incline of the road.
The tight curve of the road.
When studying the results of a baseball team, previous results of performance are looked at as well as other factors.
Determine whether the following are factors to be considered in calculating the probability of the team winning their next game:
Players' injuries.
The weather.
How well another team they aren't playing against has been playing in the competition.
How well the team played last week.
In a new study, scientists have determined that it is very likely that a recent widespread drought was caused by global warming.
Determine whether the following could be among the possible contributing factors:
Governments reducing green energy initiatives.
A steady increase in global temperatures in the lead up to the drought.
Increased burning of fossil fuels.
A rise in global temperatures during previous droughts.
Based on previous data, an insurance company determines that younger drivers are more likely to have a car accident and are therefore charged a higher premium for their insurance.
Determine whether the following are among the other factors that would be considered in calculating the insurance premium for a driver:
The number of previous accidents in which the driver has been at fault.
The driver's occupation.
Where the driver lives.
The number of speeding fines the driver has received.
The number of times the driver has received a parking ticket.
The results of a particular study state that if you exercise for at least 2 hours a week, the risk of developing heart disease is significantly reduced.
Determine whether the following factors might elevate the risk of heart disease for someone who exercises more than 2 hours a week:
Having a partner who has a heart disease.
Having an uncle who has had heart disease.
A poor diet.
Having previously had a heart condition.
One weather forecaster predicted that, based on last year’s snowfall, the chance of significant snowfall this year would be 20\%. As it turned out, there was record snowfall this year.
Determine whether the following could be indicators the forecaster ignored when making their prediction:
Higher than average rainfall this year.
Long term weather patterns.
Short term weather patterns.
Lower than average temperatures this year.
In considering whether to offer a Carpentry subject to senior students the following year, the school looked at the relative frequency of students taking the subject in the last 3 years: 55\%, 42\%, 27\%. Based on these percentages, they decided to no longer offer the subject.
Determine whether the following factors may increase the demand for the subject significantly among next year’s senior students:
An increase of other subjects on offer.
A government initiative to increase the wages of carpenters.
An increase in demand for builders and carpenters in the work force.
Fewer examinations in the Carpentry subject.