Question

for a certain class, the following data table compares how many students have a cat or a dog. what is the probability that a student chosen randomly from the class has a cat or a dog?
has a cat | does not have a cat
has a dog | 5 | 4
does not have a dog | 3 | 14

Explanation:

Step1: Find total number of students

First, we calculate the total number of students by adding up all the values in the table. The values are 5, 4, 3, and 14. So, total students = \(5 + 4 + 3 + 14 = 26\).

Step2: Find number of students with cat or dog

To find the number of students with a cat or a dog, we use the principle of inclusion - exclusion. The number of students with a dog is \(5 + 4 = 9\), the number of students with a cat is \(5 + 3 = 8\), and the number of students with both a cat and a dog is 5. So, using the formula \(n(\text{cat or dog})=n(\text{cat})+n(\text{dog})-n(\text{cat and dog})\), we get \(8 + 9 - 5 = 12\). Alternatively, we can count directly from the table: students with a dog (5 + 4) plus students without a dog but with a cat (3), so \(5 + 4 + 3 = 12\).

Step3: Calculate the probability

The probability is the number of favorable outcomes (students with cat or dog) divided by the total number of outcomes (total students). So, probability = \(\frac{12}{26}=\frac{6}{13}\).

Answer:

\(\frac{6}{13}\)