Elementary probability and sample spacesEdexcel International A Level Maths: Subtopic test

1. 1
   A fair six-sided die is rolled once. Event $A$ is 'the score is even' and event $B$ is 'the score is greater than 3'.

   (a)

   Find $P(A\cap B)$.

   [1 mark]

   • A$\frac13$
   • B$\frac12$
   • C$\frac23$
   • D$\frac16$

   (b)

   Find $P(A\cup B)$.

   [1 mark]

   • A$\frac13$
   • B$\frac23$
   • C$1$
   • D$\frac12$

   (c)

   Explain why $A$ and $B$ are not mutually exclusive.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two fair four-sided dice, each numbered 1, 2, 3 and 4, are rolled and the two scores are added.

   (a)

   Find the probability that the total score is 5.

   [1 mark]

   • A$\frac17$
   • B$\frac{3}{16}$
   • C$\frac18$
   • D$\frac14$

   (b)

   Find the probability that the total score is at least 6.

   [1 mark]

   • A$\frac{3}{16}$
   • B$\frac58$
   • C$\frac38$
   • D$\frac14$

   (c)

   Find the probability that the total score is a prime number.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a class of 40 students, 22 study French ($F$), 18 study Spanish ($S$) and 9 study both. One student is chosen at random.

   (a)

   Find the probability that the student studies French or Spanish (or both).

   [3 marks]

   (b)

   Find the probability that the student studies (i) neither language, (ii) exactly one of the languages.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Events $A$ and $B$ are such that $P(A)=0.4$, $P(B)=x$ and $P(A\cup B)=0.7$.

   (a)

   (i) Given that $A$ and $B$ are mutually exclusive, find $x$.
   (ii) Given instead that $P(A\cap B)=0.15$, find $x$.
   (iii) Find the least and the greatest possible values of $x$.

   [6 marks]

   (b)

   Given that $x=0.45$ and $P(A\cap B)=0.15$, find (i) $P(A\cap B')$, (ii) $P(A'\cap B')$. (iii) Explain, using probabilities, why $A$ and $B$ are not mutually exclusive.

   [6 marks]

   Total for question 4: 12 marks

End of questions