Question

the venn diagram below shows the preferred location for the school field trip of 130 students.
if a student is chosen at random, what is the probability that the student does not prefer the zoo?

\\(\frac{9}{13}\\)
\\(\frac{7}{13}\\)
\\(\frac{6}{13}\\)
\\(\frac{4}{13}\\)

Explanation:

⚡ Using what you learned: Venn Diagrams in Probability

Step 1: Identify the total number of students

The total number of students is given as:

$$ 130 $$

We can also verify this by adding all the regions in the Venn diagram:

$$ 40 \text{ (Zoo only)} + 20 \text{ (Both)} + 20 \text{ (Water Park only)} + 50 \text{ (Neither)} = 130 $$

Step 2: Identify students who do NOT prefer the zoo

The students who prefer the zoo are represented by the entire "Zoo" circle, which includes:

$$ 40 \text{ (Zoo only)} + 20 \text{ (Both)} = 60 $$

The students who do NOT prefer the zoo are those outside the "Zoo" circle:

$$ 20 \text{ (Water Park only)} + 50 \text{ (Neither)} = 70 $$

Alternatively, using the complement:

$$ 130 - 60 = 70 $$

Step 3: Calculate the probability

The probability that a randomly chosen student does not prefer the zoo is the number of students who do not prefer the zoo divided by the total number of students:

$$ P(\text{Not Zoo}) = \frac{70}{130} = \frac{7}{13} $$

Answer:

$$ \frac{7}{13} $$