Probability experiments and frequency

330 students from Year 10 and Year 11 take part in a competition.

number of students in Year 10: number of students in Year 11 = 1: 2

125 students win a medal.

73 of the students who win a medal are in Year 11

Complete the frequency tree.

7 330 students from Year 10 and Year 11 take part in a competition.

number of students in Year 10: number of students in Year 11 = 1: 2

125 students win a medal.

73 of the students who win a medal are in Year 11

Complete the frequency tree.

Sid and Zak each throw the same biased coin. Here is some information about their throws.

Work out the relative frequency of Heads for the 200 throws.

Which results would give the best estimate of the probability of Heads?

Tick one box.

Give a reason for your answer.

7 120 people visit a maze. 80 are children, the rest are adults.

At the start of the maze you can turn left or right. 45 children turn left. 75 people in total turn left.

Complete the frequency tree.

What fraction of the children turn left? Give your answer in its simplest form.

Beth and Lynn each spin the same biased coin a number of times. The table shows information about the results.

How many more Heads did Beth spin than Lynn?

Lynn says, “My estimate of the probability of the coin landing on Heads must be the best, because 0.35 is greater than 0.32” Is she correct? Tick a box.

Give a reason for your answer.

Beth and Lynn each spin the same biased coin a number of times. The table shows information about the results.

How many more Heads did Beth spin than Lynn?

Lynn says, “My estimate of the probability of the coin landing on Heads must be the best, because 0.35 is greater than 0.32” Is she correct? Tick a box.

Give a reason for your answer.

Archie flips a biased coin 200 times. Here is some information about the outcomes after each 50 flips.

Work out the best estimate for the probability of flipping a head. Give a reason for your answer.

Archie flips a biased coin 200 times. Here is some information about the outcomes after each 50 flips.

Work out the best estimate for the probability of flipping a head. Give a reason for your answer.

8400 fans go to a rugby match.

6850 of the fans support the Home team. The remaining fans support the Away team.

20% of the Home fans wear a scarf. 2319 of all the fans wear a scarf.

Complete the frequency tree.

On a biased dice, P(lands on 6) = 0.38

This dice is rolled 150 times.

How many times would you expect the dice not to land on 6 ?

A bag contains discs.

Trial A disc is chosen at random from the bag. The colour of the disc is noted. The disc is put back into the bag.

The trial is carried out 100 times. The table shows the relative frequency of a blue disc after every 25 trials.

For the trials from the 26th to the 50th, how many times was a blue disc chosen?

There is a total of 1000 discs in the bag.

Work out the best estimate of the number of blue discs in the bag.

8 93 people were asked if they played online games one day. The frequency tree shows some information about their answers.

75% of the people who answered Yes played one game. Complete the frequency tree.

One of the 93 people is chosen at random. P(used social media) is more than 0.68

What is the smallest possible number of people who used social media?

In a game,

an ordinary fair six-sided dice is rolled

the fair spinner shown is spun.

The score is the dice number substituted into the spinner expression.

Complete the table to show all of the possible scores.

A player wins the game if their score is 10 or more. Work out the probability that they win the game.

The game is played 711 times. Estimate the number of games that are won.

In a game,

an ordinary fair six-sided dice is rolled

the fair spinner shown is spun.

The score is the dice number substituted into the spinner expression.

Complete the table to show all of the possible scores.

A player wins the game if their score is 10 or more. Work out the probability that they win the game.

The game is played 711 times. Estimate the number of games that are won.

Here is a biased spinner.

Ali, Ben and Cary want to know the probability of spinning red on the biased spinner. They each spin it and count how many times it lands on red and divide by the total number of spins.

Who had the best estimate for the probability of spinning red? Give a reason for your answer.

Dev spins the spinner 80 times. He says, “My relative frequency of red is 0.185” Give a reason why his relative frequency must be wrong.

Elena spins the spinner 125 times. The relative frequency of red is 0.32 Work out how many times the spinner landed on green.

480 people are asked if they eat sushi. 20% say Yes. of the people who say Yes eat sushi at least once a month. Complete the frequency tree.

Here are the results after 250 spins of a coin.

The coin is spun an extra 50 times. After all 300 spins, the relative frequency of Heads is 0.49 For the extra 50 spins, work out number of Heads: number of Tails

Here are the results after 250 spins of a coin.

The coin is spun an extra 50 times. After all 300 spins, the relative frequency of Heads is 0.49

For the extra 50 spins, work out number of Heads: number of Tails

Rosie makes phone calls to try to sell broadband. Today, she made 120 calls. The table shows the results.

Write down the relative frequency that a call was not answered.

During the rest of the week, Rosie will make 500 calls. Using the results in the table, how many sales does she expect to make during the rest of the week ?

Rosie makes phone calls to try to sell broadband. Today, she made 120 calls. The table shows the results.

Write down the relative frequency that a call was not answered.

During the rest of the week, Rosie will make 500 calls. Using the results in the table, how many sales does she expect to make during the rest of the week ?

Some students were asked about their daily exercise.

12 more students answered Yes than answered No. Complete the frequency tree.

One of the 35 students who answered Yes is chosen at random. What is the probability that they exercise for at least 1 hour?

Adam and Bianca each throw the same biased coin. Here is some information about their throws.

Bianca says, ‘‘My results give a better estimate of the probability of Heads than Adam’s results.’’ Is she correct? Tick a box.

Give a reason for your answer.

A sports team played 40 games. Half were home games and half were away games. Each game was a win, a draw or a loss. Of the home games, were losses. Of the away games, were wins.

Complete the frequency tree.

The team gets 6 points for a win 3 points for a draw 0 points for a loss. Work out the total number of points that the team got.

250 trains arrived at a station. The number of trains that were late was recorded after every 50 trains. The table shows some information about the results.

Complete the relative frequency graph.

Write down the best estimate of the probability that a train arriving at the station is late.

250 trains arrived at a station. The number of trains that were late was recorded after every 50 trains. The table shows some information about the results.

Complete the relative frequency graph.

Write down the best estimate of the probability that a train arriving at the station is late.

Here are four number cards.

Use each card once to make this calculation correct.

Two of the cards are chosen at random.

List all the possible pairs of cards. Two have been done for you.

Write down the probability that the first card is an even number.

9 500 people started a race. 280 were men and the rest were women. 80% of the men finished the race. 30 women did not finish the race. Complete the frequency tree.

A record was kept of the number of days that 25 students were absent one term. The chart represents the results.

Work out the mean number of days absent.

One of the students is chosen at random. Work out the probability that the student was absent for less than 4 days.

9 56 customers pay for satellite television. They all have the Basic package for £24.50 per month. Some also have the Sports package for £27.50 extra per month the Movie package for £18 extra per month. The frequency tree shows the number of customers with each package.

In total, how much per month do the 56 customers pay?

A biased coin is thrown 250 times. The relative frequency of Heads is worked out after every 50 throws.

Circle the best estimate of the probability of Heads.

0.3 0.32 0.342 0.4

At a cinema, films are shown on Screen 1 and Screen 2 Customers pay full price or child price. There are three times as many customers in Screen 2 as Screen 1 68 customers paid child price. Complete the frequency tree.

In a game, a fair spinner has five equal sections as shown.

Chloe spins the spinner. Write down the probability that she gets ‘Miss a turn’.

The spinner lands on ‘Go back 1 square’ three times in a row. Jamal is next to spin. Write down the probability that he gets ‘Go back 1 square’.

In one game there are 85 spins. How many of these spins are expected to be ‘Go forward 2 squares’?

The probability of Heads when a biased coin is thrown is 0.6 The coin is thrown 500 times. Circle the expected number of Tails. 20 200 250 300

A coin is thrown 50 times. It lands on heads 31 times.

Write down the relative frequency it lands on heads.

Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct.

A coin is thrown 50 times. It lands on heads 31 times.

Write down the relative frequency it lands on heads.

Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct.

A biased dice is thrown. Here are the probabilities of each score.

The dice is thrown 200 times. Work out the expected number of times the score will be odd.

On three days, Ali throws darts at a target. Here are his results.

Work out two different estimates for the probability of Ali hitting the target.

Which of your two answers is the better estimate for the probability of Ali hitting the target? Give a reason for your answer.

On three days, Ali throws darts at a target. Here are his results.

Work out two different estimates for the probability of Ali hitting the target.

Which of your two answers is the better estimate for the probability of Ali hitting the target? Give a reason for your answer.

In a game, three stars are hidden at random. Each star is behind a different square on this board.

A square is chosen at random. What is the probability that there is a star behind it?

In one game, the stars are behind three consecutive squares. The squares are in one row or one column. One of the squares is E2 Write down all the possible pairs for the other two squares.

An experiment is carried out 200 times. The possible outcomes are K, L and M.

Complete the table.

Altogether, the experiment is carried out 500 times.

How many times would you expect the outcome to be K?

42 men and 38 women visit a restaurant. 44 of these people have a voucher. Three times as many men as women do not have a voucher.

Complete the frequency tree.

A voucher takes 15% off the bill. After using the voucher, the bill for a meal is £27.20 How much was the bill before using the voucher?

42 men and 38 women visit a restaurant. 44 of these people have a voucher. Three times as many men as women do not have a voucher.

Complete the frequency tree.

A voucher takes 15% off the bill. After using the voucher, the bill for a meal is £27.20 How much was the bill before using the voucher?

6 500 people are asked if they drink coffee.

20% of the people who say Yes drink at least three cups each day.

Complete the frequency tree.

What fraction of the 500 people drink at least three cups of coffee each day? Give your answer in its simplest form.

A code has 4 digits. Each digit is a number from 0 to 9 Digits may be repeated. The code starts 5 4 1

Joe chooses a number at random for the last digit. Write down the probability that he chooses the correct number.

Amy knows the last digit is odd but not 7 She chooses a different odd number at random. What is the probability that she chooses the correct number?

The table shows information about some CDs.

Work out the probability it is jazz.

List all the factors of 30

A factor of 30 is chosen at random. What is the probability that it is a 2-digit number?

A coin lands on Tails 200 times. The relative frequency of Tails is 0.4 Work out the number of times the coin was thrown.