Mutually exclusive and independent eventsEdexcel A-Level Maths: Subtopic test

1. 1
   Events $A$ and $B$ are mutually exclusive, with $P(A)=0.3$ and $P(B)=0.4$.

   (a)

   Find $P(A\cup B)$.

   [1 mark]

   • A$0.12$
   • B$0.7$
   • C$0.58$
   • D$0.1$

   (b)

   Find $P(A'\cap B')$.

   [1 mark]

   • A$0.42$
   • B$0.7$
   • C$0.3$
   • D$0.12$

   (c)

   Show that $A$ and $B$ are not independent.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Events $C$ and $D$ are independent, with $P(C)=0.6$ and $P(D)=0.25$.

   (a)

   Find $P(C\cap D)$.

   [1 mark]

   • A$0.85$
   • B$0$
   • C$0.35$
   • D$0.15$

   (b)

   Find $P(C\cup D)$.

   [1 mark]

   • A$0.7$
   • B$0.85$
   • C$0.15$
   • D$0.55$

   (c)

   Find $P(C\mid D')$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Events $A$ and $B$ are independent, with $P(A)=0.2$ and $P(A\cup B)=0.6$. Event $E$ is mutually exclusive with $A$ and also mutually exclusive with $B$, and $P(E)=0.3$.

   (a)

   Find $P(B)$.

   [3 marks]

   (b)

   Show that $B$ and $E$ are not independent, and find the probability that none of $A$, $B$ and $E$ occurs.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Events $A$ and $B$ are such that $P(A)=0.5$ and $P(A\cup B)=0.8$.

   (a)

   Let $P(B)=p$. (i) Find $p$ if $A$ and $B$ are mutually exclusive. (ii) Find $p$ if $A$ and $B$ are independent. (iii) Hence explain whether $A$ and $B$ can be both mutually exclusive and independent.

   [6 marks]

   (b)

   Given that $A$ and $B$ are independent, show that $A'$ and $B'$ are also independent.

   [6 marks]

   Total for question 4: 12 marks

End of questions