The probability that a student owns a dog is 1/3. The probability that the same student owns a dog and the cat is 2/15. Determine the probability that the student owns a cat

Assuming that the events are independent then

$$\\\frac{1}{3}\times P(Cat)=\frac{2}{15}\\\\ P(Cat)=\frac{2}{15}\div \frac{1}{3} \\\\ P(Cat)=\frac{2}{15}\times \frac{3}{1} \\\\ P(Cat)=\frac{2}{\not{15}^5}\times \frac{\not{3}^1}{1} \\\\ P(Cat)=\frac{2}{5} \\\\$$