16 A sample of 240 households were asked which, if any, of the following animals they own as pets:
- cats (C)
- dogs (D)
- tortoises ( \(T\) )
The results are shown in the table below.
| Types of pet | \(C\) | \(D\) | \(T\) | \(C\) and \(D\) | \(C\) and \(T\) | \(D\) and \(T\) | \(C , D\) and \(T\) |
| 153 | 70 | 45 | 48 | 21 | 32 | 17 |
16
- Represent this information by fully completing the Venn diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{6ad3bac9-bf08-443d-8be2-b0c26209ffe8-24_858_1191_1032_427}
16 - A household is chosen at random from the sample.
16 - Find the probability that the household owns a cat only.
16
- (ii) Find the probability that the household owns at least two of the three types of pet.
16 - (iii) Find the probability that the household owns a cat or a dog or both, given that the household does not own a tortoise.
16 - Determine whether a household owning a cat and a household owning a tortoise are independent of each other.
Fully justify your answer.