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12.06 Expected frequency

Worksheet
Expected frequency
1

A spinner is divided equally into 5 sections, with 2 sections coloured white.

a

Find the probability of landing on white.

b

If the spinner is spun 685 times, how many times would you expect it to land on white?

2

A fair die is rolled 18 times.

a

Find the probability of getting a 1 on a single roll of a die.

b

How many times would you expect a 1 to come up in the 18 rolls?

3

260 fair dice are rolled.

a

Find the probability of getting an even number on a single roll of a die.

b

How many times would you expect an even number to come up on the 260 dice?

4

If Maria rolls a die 48 times, how many twos would she expect to come up?

5

If Buzz flips a coin 96 times, how many tails would he expect to come up?

6

After flipping a fair coin 70 times, the relative frequency of heads is found to be \dfrac{52}{70}.

a

Find the probability of the next flip being a tail.

b

If the experiment were to be repeated an infinite number of times, what fraction would you expect the relative frequency of heads to be?

7

Valerie flips 3 coins at once and repeats this 40 times.

a

For each time that Valerie flips 3 coins at once, find the probability that all 3 coins show heads.

b

Hence find the probability that at least 1 of the coins shows tails.

c

How many times can she expect 3 heads to come up at once in the 40 trials?

d

How many times can she expect at least 1 tail to come up in the 40 trials?

8

Uther decided to flip a coin 14 times.

a

How many times would he expect a tail to appear?

b

After he finished flipping the coins, he noticed that tails had appeared 4 times. Find the experimental probability of getting tails.

c

Explain why the experimental probability and Uther's expectation of getting tails is not the same.

9

Dave rolls 2 dice at once and repeats this 36 times.

a

How many times can he expect the number 3 to appear in total?

b

How many times in total can he expect an even number to appear on a die?

10

Sixteen dice were rolled and a 2 occurred on four of the dice.

a

Find the probability of rolling a 2.

b

How many times would you expect a 2 to occur if 48 dice are rolled?

11

Christa rolled a die 60 times.

a

How many times would she expect a two to appear?

b

After she finished rolling the die, she noticed that she had rolled a two 26 times. Find the experimental probability of getting a two.

12

Yvonne has a bag with 3 red balls, 3 blue balls, and 3 green balls in it. Each time she took a ball out of the bag and then returned it. She repeated this 36 times.

a

How many times would she expect to get a red ball?

b

After she finished, she noticed that she had drew a red ball 12 times. Find the experimental probability of getting a red ball.

13

Georgia is drawing a card out of a deck of 10 cards, labeled from 1 to 10. She drew a card and returned it 40 times.

a

How many times would she expect to get the card with 6 on it?

b

After she finished, she noticed that she had drew the 6 card 6 times. Find the experimental probability of getting the 6 card.

14

During tennis practice, a coach focused on his player's forehands. He found that 10\% were hit into the net, 11\% were hit out of the court, and the remainder were hit in the court.

a

What percentage of the player's forehands were hit in the court?

b

If the player hits 300 forehands during the practice session, how many went into the net or out of the court?

15

The given table presents the results of multiple coin tosses with a biased coin:

HeadsTails
Frequency4753
a

How many times was the coin tossed?

b

Find the experimental probability of tossing a head.

c

Find the experimental probability of tossing a tail.

d

If this coin was tossed 1000 times, how many times would you expect it to land on a head?

e

If this coin was tossed 800 times, how many times would you expect it to land on a tail?

16

Three students were trying to determine the probability of every possible outcome when three coins are tossed. They tossed the coins and recorded the results in the given table.

a

Find the experimental probability of getting 2 heads and a tail.

b

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.

OutcomeNumber of trials resulting in outcome
\text{A: } 3 \text{ heads}17
\text{B: } 2 \text{ heads and a tail}37
\text{C: } 2 \text{ tails and a head}31
\text{D: } 3 \text{ tails}13
17

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:

a

400 times?

b

500 times?

c

600 times?

d

920 times?

HeadsTails
Frequency4456
18

Justin spun the following spinner 32 times:

a

How many times would he expect the arrow to land on X?

b

After he finished spinning, he noticed that the arrow fell on X 20 times. Find the experimental probability of getting an X.

19

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?

A
ColorFrequency
\text{Black}54
\text{Red}55
B
SuitFrequency
\text{Spade}21
\text{Heart}34
\text{Diamond}21
\text{Club}33
20

If the probability of an event occurring is \dfrac{11}{25}, how many times would you expect the event to occur in 575 trials?

21

Amelia selects a card 260 times from a standard deck of 52 cards, with replacement.

a

How many diamonds can she expect to draw?

b

How many black cards can she expect to draw?

c

How many royal cards (Kings, Queens and Jacks) can she expect to draw?

d

How many times can she expect to draw the King of diamonds?

22

800 light bulbs were tested at a factory, and 81 were found to be faulty.

a

Find the experimental probability that a light bulb at this factory will be faulty.

b

If another 1600 light bulbs were tested, how many of these would you expect to be faulty?

23

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:

a

1 ticket every week.

b

10 tickets every week.

24

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?

25

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:

a

Yellow?

b

Blue?

c

Pink?

d

Yellow or pink?

e

Blue or pink?

f

Yellow, blue or pink?

26

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?

27

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?

28

On average, about 60\% of commuters use public transport. In a sample of 200 commuters, how many would you expect to use public transport?

29

Random selections were made from a set of cards labelled from 1 to 7. The following table shows the results:

a

How many selections were made in total?

b

Find the experimental probability of drawing a 3.

c

Find the experimental probability of not drawing an odd number.

d

Find the experimental probability of drawing a number greater than 4.

e

If 1000 random selections were made, how many times would you expect to draw a number divisible by 5?

OutcomeFrequency
164
262
359
462
563
664
762
30

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:

a

How many people were surveyed?

b

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?

CandidateNumber of people
\text{A}79
\text{B}96
\text{C}93
31

The column graph shows the four countries that university students applied to for exchange in the last month:

a

What is the relative frequency of the country with the fewest applications?

b

If the monthly applications are the same throughout the year, how many people will apply for UK over the next 12 months?

32

The column graph shows the four countries that university students applied to for exchange in the last month:

a

What is the relative frequency of the country with the fewest applications?

b

If an estimate of 3000 students will apply for exchange this year, how many students will apply for exchange to Spain?

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