in a class of 23 students, 10 have a cat and 12 have a dog. there are 2 students who have a cat and a dog…

in a class of 23 students, 10 have a cat and 12 have a dog. there are 2 students who have a cat and a dog. what is the probability that a student chosen randomly from the class does not have a cat?

in a class of 23 students, 10 have a cat and 12 have a dog. there are 2 students who have a cat and a dog. what is the probability that a student chosen randomly from the class does not have a cat?

Answer

Explanation:

Step1: Find number of students with a pet

Use the principle of inclusion - exclusion. The number of students with a cat or a dog is $n(C\cup D)=n(C)+n(D)-n(C\cap D)$. Here, $n(C) = 10$ (students with a cat), $n(D)=12$ (students with a dog) and $n(C\cap D) = 2$. So $n(C\cup D)=10 + 12-2=20$.

Step2: Find number of students without a pet

The total number of students in the class is $N = 23$. The number of students without a pet is $23 - 20=3$.

Step3: Calculate the probability

The probability $P$ that a randomly - chosen student does not have a pet is $P=\frac{\text{Number of students without a pet}}{\text{Total number of students}}=\frac{3}{23}$.

Answer:

$\frac{3}{23}$