Probability experiments and frequency

120 students are asked if they have a skateboard or a scooter. 37 of the students have a skateboard. 21 of the students who have a skateboard also have a scooter. 65 of the students have a scooter.

Use this information to complete the frequency tree.

One of the 120 students is chosen at random.

Find the probability that this student does not have a skateboard.

The table shows the probabilities that a biased dice will land on 3, on 4, on 5 and on 6

Karim assumes that the probabilities that the dice will land on 1 and on 2 are the same. Karim rolls the biased dice 500 times.

Assuming Karim is right, work out an estimate for the number of times the dice will land on 2

Karim is wrong. The probability that the dice will land on 2 is greater than the probability that the dice will land on 1

How does this information affect your answer to part (a)?

The table shows the probabilities that a biased dice will land on 3, on 4, on 5 and on 6

Karim assumes that the probabilities that the dice will land on 1 and on 2 are the same. Karim rolls the biased dice 500 times.

Assuming Karim is right, work out an estimate for the number of times the dice will land on 2

Karim is wrong. The probability that the dice will land on 2 is greater than the probability that the dice will land on 1

How does this information affect your answer to part (a)?

Majid has a spinner.

Majid is going to spin the arrow. The arrow can land on 1 or on 2 or on 3 Majid says, “The probability that the arrow will land on 2 is because the spinner has three sections.” Is Majid correct? You must give a reason for your answer.

A travel agent sold 100 holidays in April. Each of these holidays was in the UK or was abroad. 64 of the 100 holidays were sold to families. The rest of the holidays were sold to couples. 11 of the 18 holidays abroad were sold to couples.

Use this information to complete the frequency tree.

One of the holidays sold to a family is chosen at random.

Find the probability that this holiday was not abroad.

Here is a biased spinner.

The table shows the probabilities that when the spinner is spun it will land on A, on B, on C and on D.

Luka will spin the spinner 200 times. Work out an estimate for the number of times the spinner will land on A.

240 people work at a factory. Of these people 150 have a car 110 have a bicycle 65 of the people who have a bicycle do not have a car.

Use this information to complete the frequency tree.

What percentage of the 150 people who have a car also have a bicycle?

A biased dice is thrown 60 times. The table shows information about the number that the dice lands on each time.

Gethin throws the dice twice.

Work out an estimate for the probability that the dice will land on 6 both times.

Sally is going to throw the same dice n times and record the number it lands on each time. She will use her results to work out a more reliable estimate for the probability in part (a).

What can you say about the value of n?

There are only blue counters, red counters and green counters in a box. The probability that a counter taken at random from the box will be blue is 0.4 The ratio of the number of red counters to the number of green counters is 7: 8 Sameena takes at random a counter from the box. She records its colour and puts the counter back in the box. Sameena does this a total of 50 times. Work out an estimate for the number of times she takes a green counter.

72 people did a test. 20 of the 32 adults who did the test passed. 6 of the children who did the test failed.

Use this information to complete the frequency tree.

One of these people is picked at random.

Find the probability that this person is an adult who failed the test.

60 people are asked if they prefer to text or to email their friends. 38 of the people are women and the rest are men. 15 of the men prefer to email their friends. 60% of the people prefer to text their friends. Complete the frequency tree for this information.

Malik is going to throw a fair coin 50 times.

Write down an estimate for the number of times the coin will land on heads.

Paula and Simon are trying to find out if a different coin is biased. Paula throws this coin 10 times. She records the number of times the coin lands on heads. Simon throws the same coin 100 times. He records the number of times the coin lands on heads.

Whose results will be more useful in deciding if the coin is biased? Give a reason for your answer.

120 people were at a hockey match.

Each person was asked if they wanted to stand or to sit to watch the match.

75 of the people were female 29 of the males wanted to stand 30 of the people wanted to sit

Use this information to complete the frequency tree.

One of the 120 people is chosen at random.

Write down the probability that this person is a male who wanted to stand.

Stuart throws a biased coin 10 times. He gets 7 Tails. Maxine throws the same coin 50 times. She gets 30 Tails. Prasha is going to throw the coin once.

Whose results will give the better estimate for the probability that she will get Tails, Stuart’s or Maxine’s? You must give a reason for your answer.

Use Stuart’s and Maxine’s results to work out an estimate for the probability that Prasha will get Tails.

Four biased coins, A, B, C and D are thrown. The probability that each coin will land on Heads is shown in the table.

Which coin is least likely to land on Heads?

Which coin is most likely to land on Heads?

Julie says, “The probability that coin C will land on Heads is the same as the probability that coin C will land on Tails.”

Is she correct? Give a reason for your answer.

Coin B is going to be thrown 4000 times.

Work out an estimate for the number of times coin B will land on Heads.

80 people are asked if they like coffee.

48 of these people are women. 61 of the 80 people like coffee. 8 of the men do not like coffee.

Use this information to complete the frequency tree.

One of the people who like coffee is chosen at random.

Find the probability that this person is a woman.

Here is a 4-sided spinner.

The table shows the probabilities that when the spinner is spun it will land on 1, on 3 and on 4

The spinner is spun once.

Work out the probability that the spinner will land on 2

Which number is the spinner least likely to land on?

Jake is going to spin the spinner 60 times.

Work out an estimate for the number of times the spinner will land on 1

Each worker in a factory is either left-handed or right-handed.

22 of the 45 workers are male. 16 of the 34 right-handed workers are female.

Complete the frequency tree for this information.

200 people live in a village.

23 people do not have a garden. 10 males do not have a garden. 95 people are male.

Use this information to complete the frequency tree.

One of the people who does not have a garden is chosen at random.

Write down the probability that this person is female.

When a drawing pin is dropped it can land point down or point up.

Lucy, Mel and Tom each dropped the drawing pin a number of times.

The table shows the number of times the drawing pin landed point down and the number of times the drawing pin landed point up for each person.

Rachael is going to drop the drawing pin once.

Whose results will give the best estimate for the probability that the drawing pin will land point up? Give a reason for your answer.

Stuart is going to drop the drawing pin twice.

Use all the results in the table to work out an estimate for the probability that the drawing pin will land point up the first time and point down the second time.

When a drawing pin is dropped it can land point down or point up.

Lucy, Mel and Tom each dropped the drawing pin a number of times.

The table shows the number of times the drawing pin landed point down and the number of times the drawing pin landed point up for each person.

Rachael is going to drop the drawing pin once.

Whose results will give the best estimate for the probability that the drawing pin will land point up? Give a reason for your answer.

Stuart is going to drop the drawing pin twice.

Use all the results in the table to work out an estimate for the probability that the drawing pin will land point up the first time and point down the second time.

The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6

Neymar rolls the biased dice 200 times.

Work out an estimate for the total number of times the dice will land on 1 or on 3