Answer:
[tex]\sf P(cat^c)=0.5[/tex]
Step-by-step explanation:
In set notation, the exponent 'c' denotes the complement of a set.
The complement of a set consists of all elements not belonging to the original set but present in the universal set.
In probability notation, P(catᶜ) represents the probability of an event not being a cat. In the context of the provided Venn diagram, this would correspond to the probability of randomly selecting an element outside the "cat" circle.
Therefore, to find P(catᶜ), sum up the numbers outside of the "cat" circle and then divide by the total sum of all numbers in the diagram:
[tex]\sf P(cat^c)=\dfrac{10+5}{10+5+7+8}\\\\\\P(cat^c)=\dfrac{15}{30}\\\\\\P(cat^c)=\dfrac{1}{2}\\\\\\P(cat^c)=0.5[/tex]
Therefore, the probability of an event not being a cat is:
[tex]\Large\boxed{\boxed{\sf P(cat^c)=0.5}}[/tex]
