Suppose that every cat is equally likely to be long-haired...I need help with part e.

3. Suppose that every cat is equally likely to be long-haired or short-haired [i.e., long-haired and short-haired cats occur in a 1:1 ratio in the population]. Bob adopted two cats, the rst one in 2010 and the second in 2011. d] Define events: L=cat is long-haired, S=cat is short-haired What is the sample space for the two cats that were adopted? What is the probability that both the cats that Bob adopted were long- haired? If we know that he adopted at least one long-haired cat, what is the probability that both were long-haired? Write the probability statement and calculate your answer. If the 2010 cat is known to be long-haired, what is the probability that both cats are long-haired? Write the probability statement and calculate your answer. Suppose at least one of the two cats is called Shadow, what is the probability that both cats are long-haired? Assume that it's possible for both cats to be named Shadow if they are long-haired, and that it's not possible for short- haired cats to be named Shadow. Also assume that the probability of being named Shadow is \"p\" for the long-haired cats. Write the probability statement and show your steps as you calculate your answer [note that your answer will be in terms of p and will not be a number). Hint: Bayes Theorem might be usell