Probability Toolkit (Edexcel IGCSE Maths): Exam Questions

Karl wants to raise money for charity. He designs a game for people to play.

Karl uses a fair 10-sided dice for the game. The dice is numbered from 1 to 10

Each person will roll the dice once. A person wins the game if the dice lands on a multiple of 4

Ali plays the game once.

Work out the probability that Ali will win the game.

Each person pays 30p to play the game once. The prize for a win is £1

Karl thinks that the game will be played 100 times.

Work out an estimate for how much money Karl will raise for charity.

One of the teachers at a school is chosen at random.

The probability that this teacher is female is $\frac{3}{5}$

There are 36 male teachers at the school.

Work out the total number of teachers at the school.

The probability that a biased dice will land on a five is 0.3

Megan is going to roll the dice 400 times.

Work out an estimate for the number of times the dice will land on a five.

There are $5$ girls, $6$ boys and some adults in a room. Jenny selects at random one of these people.

The probability that Jenny selects a girl is $\frac{1}{3}$

Work out the probability that Jenny selects an adult.

There are only red counters, blue counters, white counters and black counters in a bag.

The table shows the probability that a counter taken at random from the bag will be red or blue.

The number of white counters in the bag is the same as the number of black counters in the bag.

Tania takes at random a counter from the bag.

Work out the probability that Tania takes a white counter.

There are 240 counters in the bag.

Work out the number of red counters in the bag.

Jane has a packet of seeds. The probability that a seed will grow is 0.75

What is the probability that a seed will not grow?

Jane plants 200 of these seeds.

Estimate the number of the seeds that will grow.

There are only blue counters, yellow counters, green counters and red counters in a bag. A counter is taken at random from the bag.

The table shows the probabilities of getting a blue counter or a yellow counter or a green counter.

Work out the probability of getting a red counter.

What is the least possible number of counters in the bag? You must give a reason for your answer.

Rhiana plays a game.

The probability that she will lose the game is 0.32 The probability that she will draw the game is 0.05

Rhiana is going to play the game 200 times.

Work out an estimate for the number of times Rhiana will win the game.

There are some green counters, some yellow counters, some blue counters and some red counters in a bag.

The table shows the probabilities that a counter taken at random from the bag will be green or yellow or red.

Mary takes at random a counter from the bag.

Work out the probability that the counter will be blue.

Mary puts the counter back into the bag. There are 125 counters in the bag.

Work out the number of green counters in the bag.

Four friends each throw a biased coin a number of times. The table shows the number of heads and the number of tails each friend got.

The coin is to be thrown one more time.

Which of the four friends' results will give the best estimate for the probability that the coin will land heads? Justify your answer.

Paul says,

"With this coin you are twice as likely to get heads as to get tails."

Is Paul correct? Justify your answer.

The coin is to be thrown twice.

Use all the results in the table to work out an estimate for the probability that the coin will land heads both times.

Here is a four sided spinner. The spinner is biased.

The table shows the probabilities that the spinner will land on 1 or on 3

The probability that the spinner will land on 2 is the same as the probability that the spinner will land on 4

Work out the probability that the spinner will land on 4.

Shunya is going to spin the spinner 200 times.

Work out an estimate for the number of times the spinner will land on 3.

There are some black pens, some blue pens, some red pens and some green pens in a box.

The table shows the probabilities that a pen taken at random from the box will be black or will be blue or will be red.

There are 200 pens in the box.

Work out the number of black pens in the box.

A pen is taken at random from the box.

Work out the probability that the pen will be green.

There are 54 fish in a tank. Some of the fish are white and the rest of the fish are red.

Jeevan takes at random a fish from the tank. The probability that he takes a white fish is $\frac{4}{9}$

Work out the number of white fish originally in the tank.

Jeevan puts the fish he took out, back into the tank. He puts some more white fish into the tank.

Jeevan takes at random a fish from the tank. The probability that he takes a white fish is now $\frac{1}{2}$

Work out the number of white fish Jeevan put into the tank.

Carol spins a spinner 80 times.

The table shows information about her results.

Dan spins this spinner 300 times.

Work out an estimate for the number of times that Dan will get an L.

Here is a five-sided spinner.

The table shows the probabilities that the spinner will land on A or on B or on C or on D.

Kirsty spins the spinner once.

Work out the probability that the spinner will land on E.

Chris is going to spin the spinner 60 times.

Work out an estimate for the number of times the spinner will land either on A or on B.

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.

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.

Each time John plays a game, the probability that he wins the game is 0.65

John is going to play the game 300 times.

Work out an estimate for the number of games that John wins.

A bag contains only red beads, blue beads, green beads and yellow beads.

The table gives the probabilities that, when a bead is taken at random from the bag, the bead will be blue or the bead will be yellow.

The probability that the bead will be green is twice the probability that the bead will be red.

Sofia takes at random a bead from the bag. She writes down the colour of the bead and puts the bead back into the bag.

She does this 180 times.

Work out an estimate for the number of times she takes a red bead from the bag.

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.

A tin contains tea bags with a choice of four different flavours of tea. The four flavours of tea are Assam or Darjeeling or Nilgiri or Rize.

Sara takes at random a tea bag from the tin.

The table shows each of the probabilities that the flavour of the tea Sara takes is Assam or Darjeeling or Rize.

Work out the probability that the flavour of the tea Sara takes is Nilgiri.

Work out the probability that the flavour of the tea Sara takes is either Darjeeling or Rize.

Here is a biased 5-sided spinner.

When the spinner is spun, it can land on red, blue, green, brown or yellow.

The table gives the probabilities that the spinner lands on red or on blue or on green.

When the spinner is spun once, the probability that the spinner lands on brown is $0.06$ more than the spinner lands on yellow.

Jennie spins the spinner $150$ times.

Work out an estimate for the number of times the spinner lands on yellow.

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.

The probability that a spinner will land on blue is $0.4$

Rayyan is going to spin the spinner $280$ times. Work out an estimate for the number of times the spinner will land on blue.

ξ = {even numbers} A = {factors of 8} B = {factors of 20} List the members of the set A U B.

A number is chosen at random from set B.

Find the probability that the number is in set (A ∩ B)

There are some ice lollies in a freezer.

The flavour of each ice lolly is banana or strawberry or mint or chocolate.

Julius takes at random an ice lolly from the freezer.

The table shows the probabilities that the flavour of the ice lolly that Julius takes is banana or strawberry or chocolate.

Work out the probability that the flavour of the ice lolly that Julius takes is either strawberry or mint.

ξ = {whole numbers} A = {factors of 100} B = {multiples of 5}

List the members of the set A ∩ B.

A number is chosen at random from set A.

Find the probability it is not in set B.

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.

Toy cars are made in a factory. The toy cars are made for $15$ hours each day. $5$ toy cars are made every $12$ seconds.

For the toy cars made each day, the probability of a toy car being faulty is $0.002$

Work out an estimate of the number of faulty toy cars that are made each day.

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.

In a bag there are only red bricks, blue bricks, green bricks and orange bricks.

The number of green bricks in the bag is the same as the number of orange bricks.

Jiao takes at random a brick from the bag. The table gives the probability that Jiao takes a red brick and the probability that he takes a blue brick.

Work out the probability that Jiao takes an orange brick.

Jiao puts the brick back into the bag. There are 91 red bricks in the bag.

Jiao is going to build a tower using all the red bricks and all the blue bricks but no other bricks. The tower will be in the shape of a cuboid. There will be 4 bricks in each layer of the tower.

Work out how many layers the tower will have.

Dora has the following number cards.

She takes a card at random, replaces the card and then takes a second card. She adds the numbers on the two cards she has taken and records the total.

Complete the following table to show all of her possible totals.

Find the probability that her total is

i) an even number,

ii) a multiple of 3 or 4.

Antonio rolls two fair six-sided dice and calculates the difference between the scores. For example, if the two scores are 2 and 5 or 5 and 2 then the difference is 3.

Complete the sample space diagram to show the possible outcomes from Antonio’s dice.

Dice 2

This spinner has two grey sections, two white sections and one black section.

Vlad says

The probability of the spinner landing on black is $\frac{1}{5}$.

Explain why Vlad is not correct.

In a bag there are only red bricks, blue bricks, green bricks and orange bricks.

The number of green bricks in the bag is the same as the number of orange bricks.

Jiao takes at random a brick from the bag. The table gives the probability that Jiao takes a red brick and the probability that he takes a blue brick.

Work out the probability that Jiao takes an orange brick.

Jiao puts the brick back into the bag. There are 91 red bricks in the bag.

Jiao is going to build a tower using all the red bricks and all the blue bricks but no other bricks. The tower will be in the shape of a cuboid. There will be 4 bricks in each layer of the tower.

Work out how many layers the tower will have.

Geoff has two fair spinners.

He spins both spinners and multiplies the numbers on each spinner.

Complete the table.

Geoff wants to work out the probability that the outcome of the multiplication is an even number or a prime number. Here is his working.

Geoff is wrong. Explain his error and give the correct answer.

A biased spinner can land on green or on yellow or on brown or on pink.

The table gives the probabilities that, when the spinner is spun, it will land on green or on yellow or on brown.

Timucin spins the spinner 200 times.

Work out an estimate for the number of times the spinner lands on pink.

Jeat is growing carrots from seed in his garden. He plants 28 carrot seeds but only 12 grow.

Jeat says

The probability of one of my carrot seeds growing is $\frac{3}{7}$.

Use Jeat’s result to show that he is correct.

A farmer uses this probability to calculate how many carrot seeds he should plant to grow 10000 carrots.

(i) How many seeds should he plant?

....................... seeds [2]

(ii) Explain why it may not be sensible for the farmer to use Jeat’s experimental probability to calculate the number of seeds he should plant.

A biased spinner has three sections each of a different colour.

The table shows the probability that, when the spinner is spun once, it will land on blue or on orange or on white.

Work out the value of $x$

$x$= .................................

The spinner is spun 250 times.

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

This is a fair 5-sided spinner.

Ciara spins the spinner twice and records the product of the two scores.

i) Complete the table.

ii) Find the probability that the product is a multiple of 3.