Discrete probability distributionsEdexcel A-Level Maths: Subtopic test

1. 1
   The discrete random variable $X$ has probability distribution $P(X=x)=kx$ for $x=1,2,3,4$, where $k$ is a constant.

   (a)

   Find the value of $k$.

   [1 mark]

   • A$\frac{1}{10}$
   • B$\frac14$
   • C$\frac16$
   • D$\frac15$

   (b)

   Find $P(X\ge3)$.

   [1 mark]

   • A$0.3$
   • B$0.4$
   • C$0.9$
   • D$0.7$

   (c)

   Two independent values of $X$ are observed. Find the probability that their sum is 3.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A fair eight-sided die has faces numbered 1 to 8. The random variable $X$ is the score when the die is rolled once.

   (a)

   Find $P(X>5)$.

   [1 mark]

   • A$\frac58$
   • B$\frac38$
   • C$\frac14$
   • D$\frac12$

   (b)

   Find the probability that $X$ is a prime number.

   [1 mark]

   • A$\frac38$
   • B$\frac14$
   • C$\frac12$
   • D$\frac58$

   (c)

   The die is rolled twice. Find the probability that the first score is greater than the second.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The discrete random variable $Y$ takes the values 0, 1, 2 and 3, with $P(Y=0)=0.15$, $P(Y=1)=a$, $P(Y=2)=2a$ and $P(Y=3)=a+0.05$.

   (a)

   Find the value of $a$ and hence $P(Y\ge2)$.

   [3 marks]

   (b)

   Two independent values of $Y$ are observed. Find the probability that their sum is 3.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A fair spinner has five equal sectors numbered 1, 2, 3, 4 and 5. The random variable $X$ is the score on one spin. The spinner is spun twice and the two scores are added to give the total $T$.

   (a)

   (i) Explain why $X$ has a discrete uniform distribution and state $P(X=x)$. (ii) Show that $P(T=6)=\frac15$. (iii) Explain why $T$ does not have a discrete uniform distribution.

   [6 marks]

   (b)

   (i) Find $P(T\text{ is even})$. (ii) Find the probability that $T$ is a multiple of 3.

   [6 marks]

   Total for question 4: 12 marks

End of questions