Probability Toolkit (Cambridge O Level Maths)

A bag contains blue, red, yellow and green balls only.
A ball is taken from the bag at random.
The table shows some information about the probabilities.

Complete the table.

Abdul takes a ball at random and replaces it in the bag.
He does this 200 times.

Find how many times he expects to take a red ball.

A group of 200 people were asked which city they would like to visit next.
The table shows the results.

 
A person from the group is chosen at random.
 
Write down the probability that this person would like to visit either Paris or Tokyo next.

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.

Tanya plants some seeds.
When a seed produces flowers, the probability that the flowers are red is 0.6 and the probability that the flowers are yellow is 0.3.

Tanya has a seed that produces flowers.
 
Find the probability that the flowers are not red and not yellow.

Suleika has six cards numbered 1 to 6.

She takes one card at random, records the number and replaces the card.

[1]

[1]

The diagram shows 5 cards.

Donald chooses a card at random.

[1]

[1]

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.

A new housing estate is being planned.
There are three possible plans: and .
A survey was carried out to see which plan people preferred.
The relative frequency table shows the results.

52 people preferred plan .

Find how many people preferred plan .

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 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 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.

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 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.