Probability Diagrams (Tree & Venn Diagrams) (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

There are 32 students in a class.

5 do not study any languages. 15 study German (G). 18 study Spanish (S).

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.

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.

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.

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.

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 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 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.

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.