Probabilities from Tables & Charts (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

$\mathcal{E}=${students in a school}
$F=${students who play football}
$B=${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.

$\mathcal{E}=${odd numbers less than 30}

$A=${3, 9, 15, 21, 27}
$B=${5, 15, 25}

Complete the Venn diagram to represent this information.

A number is chosen at random from the universal set, $\mathcal{E}$.

What is the probability that the number is in the set $A\cup B$?

Here is a Venn diagram.

Write down the numbers that are in set

i) $A\cup B$

[1]

ii) $A\cap B$

[1]

One of the numbers in the diagram is chosen at random.

Find the probability that the number is in set $A\text{'}$.

The numbers from $1$ to $14$ are shown in the Venn diagram.

i) List the members of the set $A\cap B$

[1]

ii) List the members of the set $Bʹ$ 

[1]

A number is picked at random from the numbers in the Venn diagram.

Find the probability that this number is in set $A$but is not in set $B$.

A and B are two events.

Some probabilities are shown on the Venn diagram.

Work out $\mathrm{P}(\mathrm{A}\text{'}\cup \mathrm{B})$.

In a group of 200 students:

• 120 study Chemistry $\left(C\right)$,

• 90 study Geography $\left(G\right)$,

• 50 study both Chemistry and Geography.

Draw a Venn diagram to represent this information.

A student is selected at random.

Find:

(i) $P\left(C\cup G\right)$.

(ii) $P\left(\left(C\cup G\right)\text{'}\right)$.

(iii) $P\left(\left(C\cap G\right)\text{'}\right)$.

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.

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 $A$, $B$ and $\mathcal{E}$.

$\mathrm{n}(A\cup B)=23$ Find the value of $x$.

$x=$................................................

An element is chosen at random from $\mathcal{E}$.
Find the probability that this element is in $(A\cup B)\text{'}$.