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 - AQA - A-Level Maths Pure - Question 16 - 2022 - Paper 3

To determine if owning a cat and owning a tortoise are independent events, we analyze:

1. Calculate P(C):

   • Total owning cats = 153
   • Thus, $P(C) = \frac{153}{240} = 0.6375$

2. Calculate P(T):

   • Total owning tortoises = 45
   • Thus, $P(T) = \frac{45}{240} = 0.1875$

3. Calculate P(C ∩ T):

   • Total owning both = 21
   • Thus, $P(C \cap T) = \frac{21}{240} = 0.0875$

4. Now verify independence:

   • For independence, $P(C \cap T) = P(C) \times P(T)$. If this equality holds, the events are independent.

5. Calculating: $P(C) \times P(T) = 0.6375 \times 0.1875 = 0.11943$ (approx)

   • Since $P(C \cap T) = 0.0875$ and does not equal $P(C) \times P(T)$, we conclude that owning a cat and a tortoise are not independent.