Worksheets · Foundation and Higher

Sets, Venn diagrams and sample spaces

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 4 marks

   $\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$. $A$ is the set of multiples of 3 and $B$ is the set of even numbers.

   (a) List the members of $A \cap B$. (1)

   (b) How many members does $A \cup B$ have? (1)

   (c) A number is picked at random from $\xi$. Work out $P(A')$. (2)
2. Question 2Non-calculator · 2 marks

   (a) Two fair six-sided dice, each numbered 1 to 6, are rolled. Work out the probability that the product of the two scores is 12. Give a fraction in its simplest form. (2)
3. Question 3Non-calculator · 5 marks

   There are 50 students in a year group. $F$ is the set who play football and $H$ is the set who play hockey. $2x$ play football only, $x$ play both, $3x - 4$ play hockey only and 6 play neither.

   (a) A student is picked at random. Work out $P(H)$. (4)

   (b) Work out $P((F \cup H)')$. (1)