The following table shows music preferences found by a survey of the faculty at a local university. Express your answers in fraction form.

a. Find the probability that a randomly selected person from this group likes country music.
b. What is the probability that a randomly selected person from this group likes rock music and is from the North?
c. Find the probability that a randomly selected person from this group likes oldies given that they are from the South.
d. Find P(R) in decimal form. Round to two decimal places.
e. Find P(S) in decimal form. Round to two decimal places.
f. Find P(R|S) and explain if events R and S are independent or associated events.
g. Zoe and Lisa are having a disagreement about conditional probability. Zoe thinks that P(A|B)5P(B|A) for any two events A and B. Lisa says that P(A|B) and P(B|A) do not have to be equal. Pick two events from the table in problem 5 and determine who is correct.

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Northern U.S. (N) Southern U.S. (S) Total Country Music (C) Rock Music (R) 88 50 138 11 70 81 Oldies (0) 49 44 93 Total 148 164 312