Question

an animal cage is holding 6 white cats and 12 black cats. the cage door is opened slightly and two cats escape. what is the probability that a white cat escapes, followed by a black cat? submit your answer as a simplified fraction or a decimal rounded to the hundredths place. show your work here enter your answer

Explanation:

Step1: Calculate total number of cats

There are 6 white cats and 12 black cats, so the total number of cats is $6 + 12=18$.

Step2: Calculate probability of white - cat escaping first

The probability of a white cat escaping first is $\frac{6}{18}=\frac{1}{3}$ since there are 6 white cats out of 18 total cats.

Step3: Calculate probability of black - cat escaping second

After one white cat has escaped, there are 17 cats left and 12 black cats. So the probability of a black cat escaping second is $\frac{12}{17}$.

Step4: Calculate combined probability

Since these are independent - like (in the sense of sequential) events, we multiply the probabilities. The probability of a white cat escaping followed by a black cat is $\frac{1}{3}\times\frac{12}{17}=\frac{12}{51}=\frac{4}{17}\approx0.24$.

Answer:

$\frac{4}{17}\approx0.24$