Suppose that every cat is equally likely to be long-haired or short-haired (i. e., long-hared and short-haired cats occur in a 1:1 ratio in the population). Bob adopted two cats, the first one in 2010 and the second in 2011. Define events: L=cat is long-haired, S=cat is short-haired a) What is the sample space for the two cats that were adopted? b) What is the probability that both the cats that Bob adopted were longhaired? c) 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. d) 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. e) Suppose at least one of the two cats is called Shadow, what is the probability that both cats are long-haired? Assume the following: • The probability of being named Shadow is "p". • It’s possible for both cats to be named Shadow if they are long-haired. • It’s not possible for short-haired cats to be named Shadow. Write the probability statement and show your steps as you calculate your answer. Hint: Bayes Theorem might be useful.