Probability Diagrams - Tree & Venn Diagrams (CIE IGCSE Maths: Extended)

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.

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.

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.
 

At a fitness centre, the number of members using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram.

A member using the swimming pool is chosen at random.

Find the probability that this member also uses the tennis courts and the exercise machines.

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

Find the value of .

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An element is chosen at random from .

Find the probability that this element is in .

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.

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 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.

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 .

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.

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

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.