2. A school sixth form contains 150 students. 74 study mathematics, 56 study physics and 39 study economics. 14 students study all three of these subjects, 21 study mathematics & economics, 42 study mathematics and physics whilst 18 study physics and economics. Display this information using a Venn diagram. MP E 14 students study all three of these subjects 14 21 study mathematics & economics 7 42 study mathematics and physics 28 18 study physics and economics 4 74 study mathematics 25 56 study physics 10 39 study economics 14 48

3. MP E 14 7 28 4 25 10 14 48 What does the following mean? Probability a student studies mathematics

4. MP E 14 7 28 4 25 10 14 48 What does the following mean? Probability a student DOESN’T study mathematics

5. MP E 14 7 28 4 25 10 14 48 What does the following mean? Probability a student mathematics OR physics

6. MP E 14 7 28 4 25 10 14 48 What does the following mean? Probability a student mathematics AND physics

7. MP E 14 7 28 4 25 10 14 48 What does the following mean? Probability a student mathematics AND NOT economics

8. MP E 14 7 28 4 25 10 14 48 What does the following mean? GIVEN THAT the student studies economics, what is the probability they ALSO study mathematics

9. A market researcher asked 100 adults which of the three newspapers A, B, C they read. The results showed that 30 read A, 26 read B, 21 read C, 5 read both A and B, 7 read both B and C, 6 read both C and A and 2 read all three. (a) Draw a Venn diagram to represent these data.(6) One of the adults is then selected at random. Find the probability that she reads (b) at least one of the newspapers,(2) (c) only A,(1) (d) only one of the newspapers,(2) (e) A given that she reads only one newspaper. (2)

10. AB C 2 4 3 5 21 16 10 39 A market researcher asked 100 adults which of the three newspapers A, B, C they read. The results showed that 30 read A, 26 read B, 21 read C, 5 read both A and B, 7 read both B and C, 6 read both C and A and 2 read all three. (a) Draw a Venn diagram to represent these data.(6)

11. AB C 2 4 3 5 21 16 10 39 A market researcher asked 100 adults which of the three newspapers A, B, C they read. The results showed that 30 read A, 26 read B, 21 read C, 5 read both A and B, 7 read both B and C, 6 read both C and A and 2 read all three. One of the adults is then selected at random. Find the probability that she reads (b) at least one of the newspapers,(2)

12. A market researcher asked 100 adults which of the three newspapers A, B, C they read. The results showed that 30 read A, 26 read B, 21 read C, 5 read both A and B, 7 read both B and C, 6 read both C and A and 2 read all three. One of the adults is then selected at random. Find the probability that she reads (c) only A,(1) AB C 2 4 3 5 21 16 10 39

13. A market researcher asked 100 adults which of the three newspapers A, B, C they read. The results showed that 30 read A, 26 read B, 21 read C, 5 read both A and B, 7 read both B and C, 6 read both C and A and 2 read all three. One of the adults is then selected at random. Find the probability that she reads (d) only one of the newspapers,(2) AB C 2 4 3 5 21 16 10 39

14. A market researcher asked 100 adults which of the three newspapers A, B, C they read. The results showed that 30 read A, 26 read B, 21 read C, 5 read both A and B, 7 read both B and C, 6 read both C and A and 2 read all three. One of the adults is then selected at random. Find the probability that she reads (e) A given that she reads only one newspaper. (2) AB C 2 4 3 5 21 16 10 39