1.1. The director of a company that sells smartphones wants to investigate the selling of additional features. The additional features available are: premium insurance $(I)$, cloud storage $(C)$ and screen protection $(S)$.

Last week,

• 90 smartphones were sold

• 3 smartphones were sold with premium insurance, cloud storage and screen protection

• 8 smartphones were sold with cloud storage and screen protection only

• 2 smartphones were sold with premium insurance and screen protection only

• 11 smartphones were sold with premium insurance and cloud storage only

• 14 smartphones were sold with cloud storage only

• 52 smartphones in total were sold with screen protection

• 21 smartphones in total were sold with premium insurance

Complete the Venn diagram using this information.

1.2. Siobhan picks at random a smartphone that was sold last week.

She thinks that the probability the smartphone has screen protection given that it has cloud storage, is greater than the probability that the smartphone has screen protection given than it does not have cloud storage.

Is Siobhan correct?
You must show your working.

1.3. The company also sells smart TVs, both new and second-hand.

The company director records whether the smart TVs were new or second-hand and whether or not a fault with the TV was reported within 1 year after being sold.

The table gives information about the smart TVs sold by the company in January 2023.

Eric says that the relative risk of a second-hand smart TV developing a fault within 1 year of being sold, compared with a new smart TV developing a fault within 1 year of being sold, is 3

(i) Show that Eric is correct.

[2]

(ii) Interpret a relative risk of 3 in this context.

[1]