Consider the event ray is in the garage and the event felix, Ask an Expert

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"I have 2 cats, Ray and Felix, who behave independently of one another. I know that at 4:00 pm there is a 0.9 chance that Ray will be in my garage and a 0.4 chance that Felix will be in my garage.

(a) If I walk into my garage some day at 4:00 pm, what is the probability that at most one cat will be there?
(b) Consider the event "Ray is in the garage" and the event "Felix is not in the garage." Are these events mutually exclusive?
(c) Consider the random variable Y which represents the number of cats I find in my garage at 4:00 pm. Determine the distribution of Y (Hint: Start by writing out the sample space.)
(d) What is the mean number of cats in my garage at 4:00 pm?

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