Question

if a student is chosen at random, what is the probability that the student does not prefer the zoo?

Explanation:

Step1: Calculate total number of students

The total number of students is the sum of the numbers in the V - enn diagram regions, so $40 + 20+20=80$.

Step2: Calculate number of students who don't prefer zoo

The number of students who don't prefer the zoo is the number of students who only prefer the water - park, which is 20.

Step3: Calculate the probability

The probability $P$ that a student does not prefer the zoo is the number of students who don't prefer the zoo divided by the total number of students. So $P=\frac{20}{80}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$