The probability scale

A bus is due to arrive at a bus stop at 1 pm The probability that the bus is on time is halved when it is raining.

Complete the tree diagram.

Work out the probability that at 1 pm it is raining and the bus is not on time.

Two spinners each have only red sections and green sections.

Complete the tree diagram.

Both spinners are spun.

Work out the probability that both spinners land on red.

The five possible outcomes of an event are A, B, C, D and E. The table shows some of the probabilities.

P(C) = P(B) + 0.1

P(D) = P(E)

Work out P(D)

A box contains cards that are either red, blue, green or yellow.

P(green) = P(yellow)

Complete the table.

There are 600 cards in the box. How many cards are not blue?

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.

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.

There are 56 cubes in a box. The cubes are green, red, blue or white. 17 cubes are green. There are an equal number of red, blue and white cubes.

How many red cubes are in the box?

24 more cubes are added to the box. A cube is picked at random. The probability that the cube is green is 0.4

How many of the 24 cubes added to the box are green?

Bag A and bag B contain counters.

Complete the tree diagram.

One counter is taken at random from each bag.

Work out the probability that one is red and one is white.

A fair spinner has six equal sections, each with the number 5, 6, 7 or 8 Each number appears at least once. P(even number) = P(7)

Work out P(5) You may use the blank spinner to help you.

A different spinner has ten sections, each labelled A, B, C or D.

Give one reason why there must be a mistake in the table.

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.

A fair spinner has six equal sections, each with the number 5, 6, 7 or 8 Each number appears at least once. P(even number) = P(7)

Work out P(5) You may use the blank spinner to help you.

A different spinner has ten sections, each labelled A, B, C or D.

Give one reason why there must be a mistake in the table.

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 ?

Cards are either gold or not gold. P(gold) = 0.05 Harim chooses a card at random and replaces it. He then chooses a second card.

Complete the tree diagram.

What is the probability that at least one of Harim’s cards is gold?

Jing rolls a fair six-sided dice 72 times.

Is the relative frequency of rolling a 5 greater than the theoretical probability? Tick a box.

Give a reason for your answer.

There are 1400 students at a college. A student is chosen at random.

The probability that the student is taking a GCSE resit is 0.09

How many of the students are taking a GCSE resit?

The probability that the student is studying A-levels is 0.67 Core Maths is 0.48

Show that some students are studying A-levels and Core Maths.

100 people were asked about the distance they travel from home to work. The table shows information about the results.

Distance, d (miles)	Frequency
0 d 5	21
5 d 10	24
10 d 20	37
20 d 40	18

Write down the greatest possible number of people who work from home.

One person is chosen at random.

Work out the probability that the person travels at least 10 miles.

The table is repeated.

Distance, d (miles)	Frequency
0 d 5	21
5 d 10	24
10 d 20	37
20 d 40	18

Draw a histogram to represent the results.

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?

A fair spinner with five sections is spun.

Complete these statements.

Two different spinners are spun. One spinner has sections labelled with colours. The other spinner has sections labelled with numbers. Here is a list of all the possible outcomes.

Show the possible sections on the two spinners.

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.

Three groups of people, A, B and C, have taken driving tests.

Here is information about the number of tests taken by the people in A.

Here is information about the number of tests taken by the people in B. One test Half the number in A who have taken one test. Two tests 4 fewer than the number in A who have taken two tests. Three tests 10 more than the number in A who have taken three tests. Complete this pictogram for the people in B.

In group C there are 25 people. 17 of these people have passed a test. One person is picked at random from C. Work out the probability that the person has not passed a test.

40 students were asked the number of visits they made to a gym one week. The chart shows information about the results.

Write down the modal number of visits.

Work out the mean number of visits. Give your answer as a decimal.

One of the 40 students is chosen at random. Work out the probability that the student visited the gym at least once.

A fair, ordinary dice is rolled and a counter is taken at random from a bag. The tree diagram shows the probabilities.

How do the probabilities show that all the counters in the bag are red, blue or green?

Circle the probability that the counter is red or blue.

0.0009 0.8 0.03 0.4

Circle the probability that the dice lands on an even number and the counter is blue.

0.15 0.3 0.35 0.8

In a bag there are only red discs, blue discs and green discs. There are 10 red discs. When one disc is picked at random

How many green discs are in the bag?

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 ?

Counters in a bag are red, white or blue. A counter is picked at random. Complete the table.

A biased spinner can land on A, B or C. The table shows the probabilities, in terms of k, of A, B and C.

Work out the probability of B.

Bags X and Y each contain counters.

P(green counter from X) = P(red counter from Y) Work out the number of green counters in X.

All 35 counters are put into one bag. One counter is picked at random. Work out the probability that the counter is not red.

A spinner can land on red, blue or green. After 350 spins relative frequency of red = 0.18 relative frequency of blue = 0.62 Work out the number of times the spinner landed on green.

In a raffle, 200 tickets are sold. The tickets are either red or blue. The winning ticket is picked at random.

What is the probability that the winning ticket is green?

79 children and 90 women buy one ticket each. Men buy the rest of the tickets. Work out the probability that a man buys the winning ticket.

An ordinary fair dice is rolled.

Which could be a correct statement about event A? Tick one box.

The result of a game is Win, Lose or Draw. After 80 games relative frequency of the result Win is 0.4 relative frequency of the result Lose is 0.25 How many of the games had the result Draw?

A packet contains 80 sweets. The flavour of each sweet is lemon, orange or apple. A sweet is taken at random.

P(lemon or orange) 0.85 Work out the minimum possible number of apple sweets in the packet.

P(lemon or apple) 0.71 There are 31 lemon sweets. Work out the maximum possible number of apple sweets in the packet.

In a choir there are 35 men and 48 women. The probability that a man chosen at random wears glasses is The probability that a woman chosen at random wears glasses is

Work out the number of people in the choir who wear glasses.

A person is chosen at random from the choir. Work out the probability that the person does not wear glasses.

Circle the relative frequency that represents 13 successes out of 50 trials.

0.13 26 13: 50 0.26

A fair dice has six sides, numbered 1 to 6 After it is rolled, five of the numbers can be seen.

Write down the probability that one of these five numbers is 2

Work out the greatest possible sum of the five numbers.

The probability that A is the outcome of an experiment is 0.2 Circle the probability that A is not the outcome.

0 0.2 0.5 0.8

A bus can be early, on time or late. The probability that the bus is early is 0.1 The probability that the bus is on time is 0.6 Work out the probability that the bus is late.

A fair spinner has 12 equal sections. Label each section A, B, C or D so that when the arrow is spun,

the probability it lands on B is equal to the probability it lands on C the probability it lands on D is double the probability it lands on A.

The table shows information about some CDs.

Work out the probability it is jazz.

There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is The probability that a girl chosen at random studies French is

Work out the number of students in the school who study French.

Work out the probability that a student chosen at random from the whole school does not study French.

There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is The probability that a girl chosen at random studies French is

Work out the number of students in the school who study French.

Work out the probability that a student chosen at random from the whole school does not study French.