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

A soccer team plays two matches.
The tree diagram shows the probability of the team winning or losing the matches. 

Find the probability that the soccer team wins at least one of the two matches.

{students in a school}
{students who play football}
{students who play baseball}
 
There are 240 students in the school.
 
• 120 students play football
• 40 students play baseball 
• 90 students play football but not baseball.

Complete the Venn diagram to show this information.
 

A student in the school is chosen at random.
 
Find the probability that this student plays baseball but not football.

The Venn diagram below shows information about the number of gardeners who grow melons ( ), potatoes ( ) and carrots ( ).

A gardener is chosen at random from the gardeners who grow melons.
 
Find the probability that this gardener does not grow carrots.

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 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 .

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.