Question

in a class of 24 students, 14 have a cat and 5 have a dog. there are 2 students who have a cat and a dog. what is the probability that a student has a cat given that they do not have a dog?

Explanation:

Step1: Find students with only cat

Students with only cat = Cat owners - Both owners = $14 - 2 = 12$

Step2: Find students without dog

Students without dog = Total - Dog owners = $24 - 5 = 19$

Step3: Calculate conditional probability

Probability = $\frac{\text{Only cat}}{\text{No dog}} = \frac{12}{19}$

Answer:

$\frac{12}{19}$