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

On any day the probability that it rains is .

When it rains the probability that Amira goes fishing is .
When it does not rain the probability that Amira goes fishing is .

In a period of 60 days on how many days is it expected to rain?

Complete the tree diagram.

Find the probability that on any day Amira goes fishing.

There are 32 students in a class.

Complete the Venn diagram to show this information.

A student is chosen at random.
 
Find the probability that the student studies Spanish but not German.

A student who studies German is chosen at random.

Find the probability that this student also studies Spanish.

A box contains 15 red pencils, 8 yellow pencils and 2 green pencils.
Two pencils are picked at random without replacement.

Find the probability that at least one pencil is red.

The speed,  km/h, of each of 200 cars passing a building is measured. 
The table shows the results.

Speed ( km/h)
Frequency

Two of the 200 cars are chosen at random.
 
Find the probability that they both have a speed greater than 50 km/h.

Ravi has a bag which contains 10 red balls and 8 blue balls.
Ravi takes two balls at random from his bag, without replacement.
 
Find the probability that one ball is red and one ball is blue.

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

Two people are chosen at random from the group of 200.
 
Find the probability that one person would like to visit London next and the other person would like to visit New York next.
Give your answer as a percentage.
 

............................................ %

A box contains 20 packets of potato chips.
6 packets contain barbecue flavoured chips.
10 packets contain salt flavoured chips.
4 packets contain chicken flavoured chips.
Maria takes two packets at random without replacement.

Show that the probability that she takes two packets of salt flavoured chips is

A and B are two events.

Some probabilities are shown on the Venn diagram.

Work out .

Machine A and machine B make bottles.

The probability that a bottle made by machine A is faulty is 0.02
The probability that a bottle made by machine B is faulty is 0.05

Complete the probability tree diagram.

Shazia takes at random one bottle made by machine A and one bottle made by machine B.

Work out the probability that at least one of these bottles is faulty.

Two ordinary fair dice are rolled.

Complete the tree diagram.

Work out the probability that both dice land on a number less than 3.

Work out the probability that exactly one of the dice lands on a number less than 3.

The heights, metres, of the 120 boys in an athletics club are recorded.
The table shows information about the heights of the boys.

Height ( metres)
Frequency	7	18	30	24	27	14

Three boys are chosen at random from the club.

Calculate the probability that one of the boys has a height greater than 1.8 m and the other two boys each have a height of 1.4 m or less.

On any Saturday, the probability that Bob plays football is
 
Calculate the probability that Bob plays football for 2 of the next 3 Saturdays.

On any Saturday, the probability that Arun plays football is 
When Arun plays football, the probability that he scores the winning goal is
 
Calculate the probability that Arun scores the winning goal one Saturday.

Talika has a bag which contains 10 red balls and 8 blue balls.
Talika takes three balls at random from her bag, without replacement.
 
Calculate the probability that the three balls are the same colour.

A box contains 20 packets of potato chips.
6 packets contain barbecue flavoured chips.
10 packets contain salt flavoured chips.
4 packets contain chicken flavoured chips.
Maria takes two packets at random without replacement.

Find the probability that she takes two packets of different flavoured chips.

Sonia has a bag containing 20 sweets.
In the bag, there are 5 red, 6 green and 9 yellow sweets.
Sonia chooses two sweets at random, without replacement, from the bag.

i)

Show that the probability that she chooses two green sweets is .

[2]

[4]

A darts team is going to play a match on Saturday and on Sunday.
The probability that the team will win on Saturday is 0.45

If they win on Saturday, the probability that they will win on Sunday is 0.67
If they do not win on Saturday, the probability that they will win on Sunday is 0.35

Complete the probability tree diagram.

Find the probability that the team will win exactly one of the two matches.

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

Two of the six discs are picked at random with replacement.

Find the probability that both discs have the same colour.

This year, 40 students have each travelled by one or more of plane (), train () or boat ().

7 have travelled only by plane.
11 have travelled only by train.
9 have travelled only by boat.

Complete the Venn diagram.

Two students are chosen at random.

Calculate the probability that they both have travelled only by plane.

The probability that the school bus is late is .
If the school bus is late, the probability that Seb travels on the bus is .
If the school bus is on time, the probability that Seb travels on the bus is .

Find the probability that Seb travels on the bus.

A box contains 20 packets of potato chips.
6 packets contain barbecue flavoured chips.
10 packets contain salt flavoured chips.
4 packets contain chicken flavoured chips.
 
Maria takes three packets at random, without replacement, from the 20 packets.

Find the probability that she takes at least two packets of chicken flavoured chips.

The probability that it will rain tomorrow is .
If it rains, the probability that Rafael walks to school is .
If it does not rain, the probability that Rafael walks to school is .

Complete the tree diagram.

Calculate the probability that it will rain tomorrow and Rafael walks to school.

Calculate the probability that Rafael does not walk to school.

Box A and box B each contain blue and green pens only.
Raphael picks a pen at random from box A and Paulo picks a pen at random from box B.
The probability that Raphael picks a blue pen is .
The probability that both Raphael and Paulo pick a blue pen is .

Find the probability that Paulo picks a blue pen.

Find the probability that both Raphael and Paulo pick a green pen.

The diagram shows two sets of cards.

Lena chooses three cards at random from Set C without replacement.

Find the probability that the third card chosen is numbered 4.