Probability Diagrams : Tree & Venn Diagrams (Cambridge O Level Maths)

Morgan picks two of these letters, at random, without replacement.

Find the probability that he picks two letters that are the same.

the marbles are both red,
 

[2]

the marbles are not both red.
 

[1]

40 children were asked if they have a computer or a phone or both.
The Venn diagram shows the results.

A child is chosen at random from the children who have a computer.
 
Write down the probability that this child also has a phone.

Complete the Venn diagram.
 

The Venn diagram shows information about the number of elements in sets , and .

Find the value of .

................................................

An element is chosen at random from .

Find the probability that this element is in .

Items made at a factory have to pass two checks.

90% pass the first check.
The items that fail are scrapped.
99% of the items that pass the first check pass the second check.
The items that fail are scrapped.

Complete the tree diagram.

An item is chosen at random before the checks.

Work out the probability that the item is scrapped.

The diagram shows six discs.
Each disc has a colour and a number.

Two of the six discs are picked at random without replacement.

Find the probability that 

Tanya plants some seeds.
The probability that a seed will produce flowers is 0.8.
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.

Complete the tree diagram.

Find the probability that a seed chosen at random produces red flowers.

Tanya chooses a seed at random.
 
Find the probability that this seed does not produce red flowers and does not produce yellow flowers.

Two of the seeds are chosen at random.
 
Find the probability that one produces flowers and one does not produce flowers.

Calculate the probability that Harris takes no more than three attempts to pass the driving test.

Esme has a bag with 5 green counters and 4 red counters.
She takes three counters at random from the bag without replacement.
 
Work out the probability that the three counters are all the same colour.

Bag A contains 3 black balls and 2 white balls.
Bag B contains 1 black ball and 3 white balls.
A ball is taken at random from each bag.

[1]

[3]

The balls are returned to their original bags.
Three balls are taken at random from bag A, without replacement.

[2]

[1]

The balls are returned to their original bags.
A ball is taken at random from bag A and its colour is recorded.
This ball is then placed in bag B.
A ball is then taken at random from bag B.
 
Find the probability that the ball taken from bag B has a different colour to the ball taken from bag A.

Anna plays a game with an ordinary, fair dice.

If she rolls 1 she wins.
If she rolls 2 or 3 she loses.
If she rolls 4, 5 or 6 she rolls again.

When she has to roll again,

if she rolls an odd number she wins
if she rolls an even number she loses.

Complete the tree diagram with the four missing probabilities.

Is Anna more likely to win or to lose?

You must work out the probability that she wins.

On Friday, Greg takes part in a long jump competition.
He has to jump at least 7.5 metres to qualify for the final on Saturday.

• He has up to three jumps to qualify.
• If he jumps at least 7.5 metres he does not jump again on Friday.

Each time Greg jumps, the probability he jumps at least 7.5 metres is 0.8
Assume each jump is independent.

Complete the tree diagram.

Work out the probability that he does not need the third jump to qualify.

Morgan picks three of these letters, at random, without replacement.

Find the probability that

Suleika has six cards numbered 1 to 6.

Suleika takes two cards at random, without replacement.

[3]

[3]

The diagram shows 5 cards.

Donald chooses two of the five cards at random, without replacement.
He works out the total number of dots on these two cards.

[3]

[3]

The probability that Andrei cycles to school is .

Write down, in terms of , the probability that Andrei does not cycle to school. 

The probability that Benoit does not cycle to school is .
The probability that both Andrei and Benoit do not cycle to school is .

Angelo has a bag containing 3 white counters and black counters.
He takes two counters at random from the bag, without replacement.

Complete the following statement.
 
The probability that Angelo takes two black counters is

The probability that Angelo takes two black counters is .