1. Suppose A and B are two independent events, so by definition P(A N B) = P(A)P(B). a. Prove that A and BC are independent, and that AC and BC are independent. b. Using the above facts to fill in the blanks for following contingency table, under the assumption that for a randomly selected person, the event of "being right-handed" is independent from the event “my favorite color is red." (Note: 0.360 is the probability that you are right- handed and your favorite color is red, etc.) Favorite Color Red Favorite Color Not Red Right-handed: Left-handed: 0.360 0.036 c. If "RH" refers to the event of being right-handed and "R" refers to the event that your favorite color is red, compute P(R), P(RC), P(RH), P(RHC), and P(RHUR).

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A: Solution: The given table of data is

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A: This is a fact of probability related to independent events . This is very useful in statistics .