Probability Toolkit (AQA GCSE Maths)

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

The probability that this teacher is female is 

There are 36 male teachers at the school.

Work out the total number of teachers at the school.

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.

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.

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.

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.

Lorna carries out a survey about the number of times customers go to a shop.

She asks at random 100 customers how many times they went to the shop last month.

The table shows Lorna's results.

 
One of the 100 customers is chosen at random.

What is the probability that this customer went to the shop 5 or more times?

Last month the shop had a total of 1500 customers.

Work out an estimate for the number of customers who went to the shop exactly 2 times last month.

The owner of a different shop is carrying out a survey on the ages of his customers.
He records the ages of the first 10 customers in his shop after 9 am one morning.

This may not be a suitable sample.

Give two reasons why.

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.

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

The table shows the probabilities of picking at random a red counter and picking at random a yellow counter.

The probability of picking a blue counter is the same as the probability of picking a green counter.

Complete the table.

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.

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 table gives information about the amounts of money, in euros, that 70 of Anjali’s friends spent last Saturday.

Money spent (S euros)	Frequency
	6
	14
	19
	25
	6

One of Anjali’s 70 friends is going to be chosen at random.

Find the probability that this friend spent more than 24 euros last Saturday.

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

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

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

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.

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

Bill has some counters in a bag.

of the counters are red.
of the counters are blue.
The rest of the counters are yellow.

Bill takes at random a counter from the bag.

The probability that he takes a yellow counter is 

How many yellow counters are in the bag before Bill takes a counter?

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.

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

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

The table shows the probability that Olga will take a blue counter and the probability that she will take a yellow counter.

The number of red counters in the bag is 4 times the number of green counters in the bag.

Complete the table.

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

The probability that Jenny selects a girl is 

Work out the probability that Jenny selects an adult.

There are only blue cubes, yellow cubes and green cubes in a bag.

There are

Hannah takes at random a cube from the bag.

Work out the probability that Hannah takes a yellow cube.

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.

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.

There are only red counters, blue counters and purple counters in a bag.
The ratio of the number of red counters to the number of blue counters is 3 : 17

Sam takes at random a counter from the bag.
The probability that the counter is purple is 0.2

Work out the probability that Sam takes a red counter.

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.

In a bag there are blue discs, green discs and white discs.

There are four times as many blue discs as green discs.
number of blue discs : number of white discs = 3 : 5

One disc is selected at random.

Work out the probability that the disc is either blue or white.

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

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

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

There are  counters in a bag.
Each counter in the bag is either red or blue so that

the number of red counters : the number of blue counters = 

 is going to put some more red counters in the bag so that

the probability of taking at random a red counter from the bag is 

Work out the number of red counters that is going to put in the bag.

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.

Number	1	2	3	4	5	6
Probability		0.18			0.26

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.

A bag contains only pink sweets, white sweets, green sweets and red sweets.

The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.

The ratio

number of pink sweets : number of white sweets = 2 : 1

There are 28 red sweets in the bag.

Work out the number of white sweets in the bag.

Grace has a biased 5-sided spinner.

Grace is going to spin the arrow on the spinner once.

The table below gives the probabilities that the spinner will land on red or on blue or on green.

The probability that the spinner will land on orange is 3 times the probability that the spinner will land on pink.

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

Grace spins the arrow on the spinner 150 times.

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

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.

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.

Colour	red	blue	green	brown	yellow
Probability

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

Jennie spins the spinner  times.

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

A bag contains some counters.

• There are 300 counters in the bag.
• There are only red, white and blue counters in the bag.
• The probability of picking a blue counter is 
• The ratio of red counters to white counters is 2 : 1.

Calculate the number of red counters in the bag.