Question 7

7.1 An entire sample space is made up of two complementary events, S and T, where P(S’) = 0,33.

7.1.1 Complete the statement: P(S) + P(T) = … (1)

7.1.2 Write down the value of P(T). (1)

7.2 A survey was conducted among 180 residents of a small town to establish how many people contracted tuberculosis (TB) and/or human immunodeficiency virus (HIV) during the last 5 years. The results were as follows:

• 𝑥 people were diagnosed with TB
• 30 people were diagnosed with both TB and HIV
• 69 people were HIV positive
• 51 people did not have either disease

7.2.1 Represent the information above in a Venn diagram. (4)

7.2.2 How many people contracted TB only? (3)

7.2.3 Calculate the probability that a person selected at random:

(a) Will only have been diagnosed with TB (2)

(b) Will not have any of the two diseases (1)

[12]

TOTAL: 100