The probability scale

There are only red counters, white counters, blue counters and green counters in a bag. Chris is going to take at random a counter from the bag. The table shows the probability that he will take a red counter and the probability that he will take a white counter.

There are twice as many blue counters as there are green counters in the bag.

Work out the probability that Chris will take a blue counter.

There are 45 red counters in the bag.

Work out the total number of counters in the bag.

There are only red counters, white counters, blue counters and green counters in a bag. Chris is going to take at random a counter from the bag. The table shows the probability that he will take a red counter and the probability that he will take a white counter.

There are twice as many blue counters as there are green counters in the bag.

Work out the probability that Chris will take a blue counter.

There are 45 red counters in the bag.

Work out the total number of counters in the bag.

The histogram gives information about the weights, in grams, of some biscuits.

One of these biscuits is taken at random. Work out an estimate for the probability that the biscuit will have a weight between 20 grams and 40 grams.

Tom has a fair ordinary dice. He rolls the dice once.

On the probability scale below, mark with a cross () the probability that Tom gets the number 2

On the probability scale below, mark with a cross () the probability that Tom gets a number greater than 4

Here are the ages, in years, of 8 children. 14 10 10 13 15 9 15 10

Work out the mean age.

Work out the range of the ages.

One of the children is chosen at random.

On the probability scale below, mark with a cross () the probability that this child has an age of 15

There are only £10 notes and £20 notes in a wallet. Ali takes at random a note from the wallet.

Write down the probability that Ali takes a note with a value of more than £5

There are only 1p coins and 2p coins in a bag. The total value of the coins in the bag is 40p The total value of the 1p coins is the same as the total value of the 2p coins. Simon takes at random a coin from the bag.

Find the probability that Simon takes a 1p coin.

There are only red discs, blue discs and yellow discs in a bag. There are 24 yellow discs in the bag. Mel is going to take at random a disc from the bag. The probability that the disc will be yellow is 0.16 the number of red discs: the number of blue discs = 5: 4 Work out the number of red discs in the bag.

There are only red discs, blue discs and yellow discs in a bag. There are 24 yellow discs in the bag. Mel is going to take at random a disc from the bag. The probability that the disc will be yellow is 0.16 the number of red discs: the number of blue discs = 5: 4 Work out the number of red discs in the bag.

Selina has a bag of 22 counters. 5 of the counters are blue. 9 of the counters are red. 8 of the counters are pink. Selina takes at random a counter from the bag. Write down the probability that Selina

takes a red counter,

does not take a pink counter,

takes a white counter.

Rima is going to roll a fair 6‑sided dice.

Choose the word that best describes the probability that the dice will land on the

Choose the word that best describes the probability that the dice will land on an odd number.

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.

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.

Alan grew 80 plants of the same type outside. The cumulative frequency graph shows information about the heights, in cm, of these plants.

One of the plants is chosen at random.

Find an estimate for the probability that this plant will have a height greater than 90 cm.

Use the graph to find an estimate for the median height.

Use the graph to find an estimate for the interquartile range of the heights.

Alan also grew plants of the same type inside. The interquartile range of the heights of these plants is 30 cm.

Give one comparison between the distribution of the heights of the plants grown inside with the distribution of the heights of the plants grown outside.

Shari has a fair ordinary dice. She rolls the dice once.

On the probability scale, mark with a cross () the probability that Shari gets the number 7

On the probability scale, mark with a cross () the probability that Shari gets an even number.

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?

Here is a 4-sided spinner.

Samina spins the spinner once.

Choose the word that best describes the probability that the spinner lands on 2

Choose the word that best describes the probability that the spinner lands on a

Ralph rolls a biased dice once. The probability that he gets the number 5 is 0.4

Work out the probability that Ralph does not get the number 5

Here is a list of 8 letters. B C A A A A B A

Write down the mode.

One of the 8 letters is going to be picked at random.

On the probability scale, mark with a cross () the probability that this letter will be B.

Find the probability that this letter will be C.

Lina spins a biased 5-sided spinner 40 times.

Here are her results.

Lina is now going to spin the spinner another two times.

Work out an estimate for the probability that she gets a score of 5 both times.

Derek is going to spin the spinner a large number of times.

Work out an estimate for the percentage of times Derek can expect to get a score of 1

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.

Here is a list of 8 numbers. 2 2 3 5 6 6 8 9 Kim picks at random one of these numbers.

On the probability scale below, mark with a cross () the probability that Kim picks a number 7

On the probability scale below, mark with a cross () the probability that Kim picks a number greater than 5

Find the probability that Kim picks an even number.

In a bag there are only red counters, blue counters, green counters and pink counters. A counter is going to be taken at random from the bag. The table shows the probabilities of taking a red counter or a blue counter.

The probability of taking a green counter is 0.2 more than the probability of taking a pink counter.

Complete the table.

There are 18 blue counters in the bag.

Work out the total number of counters in the bag.

In a bag there are only red counters, blue counters, green counters and pink counters. A counter is going to be taken at random from the bag. The table shows the probabilities of taking a red counter or a blue counter.

The probability of taking a green counter is 0.2 more than the probability of taking a pink counter.

Complete the table.

There are 18 blue counters in the bag.

Work out the total number of counters in the bag.

Gita spins a fair 8‑sided spinner.

On the probability scale, mark with a cross (X) the probability that the spinner will land on C.

On the probability scale, mark with a cross (X) the probability that the spinner will land on D.

There are some counters in a bag. The counters are blue or green or red or yellow. The table shows the probabilities that a counter taken at random from the bag will be blue or will be green.

The probability that a counter taken at random from the bag will be red is five times the probability that the counter will be yellow. There are 300 counters in the bag. Work out the number of yellow counters in the bag.

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.

There are only blue cubes, red cubes and yellow cubes in a box. The table shows the probability of taking at random a blue cube from the box.

The number of red cubes in the box is the same as the number of yellow cubes in the box.

Complete the table.

There are 12 blue cubes in the box.

Work out the total number of cubes in the box.

There are only blue cubes, red cubes and yellow cubes in a box. The table shows the probability of taking at random a blue cube from the box.

The number of red cubes in the box is the same as the number of yellow cubes in the box.

Complete the table.

There are 12 blue cubes in the box.

Work out the total number of cubes in the box.

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.

An ordinary fair dice is thrown once.

On the probability scale below, mark with a cross () the probability that the dice lands on an odd number.

Write down the probability that the dice lands on a number greater than 4

Here is a probability scale. It shows the probability of each of the events A, B, C and D.

Write down the letter of the event that is certain.

Write down the letter of the event that is unlikely.

There are 12 counters in a bag.

3 of the counters are red. 1 of the counters is blue. 2 of the counters are yellow. The rest of the counters are green.

Caitlin takes at random a counter from the bag.

Show that the probability that this counter is yellow or green is

Here are the marks 20 students got in a French test.

Show this information in a stem and leaf diagram.

One of these students is going to be chosen at random.

The pass mark in the French test is 71

Omar writes, The probability that this student failed the French test is

Omar is wrong.

Explain why.

There are some counters in a bag. The counters are red or white or blue or yellow.

Bob is going to take at random a counter from the bag.

The table shows each of the probabilities that the counter will be blue or will be yellow.

There are 18 blue counters in the bag.

The probability that the counter Bob takes will be red is twice the probability that the counter will be white.

Work out the number of red counters in the bag.

A marble is going to be taken at random from a box of marbles. The probability that the marble will be silver is 0.5

There must be an even number of marbles in the box.

Explain why.

Sammy spins a fair 4-sided spinner.

On the probability scale, mark with a cross (×) the probability that the spinner will land on B.

On the probability scale, mark with a cross (×) the probability that the spinner will land on F.