Problem
Suppose that a six-sided die is "loaded" so that any particular even-numbered face is twice as likely to land face up as any particular odd-numbered face. Consider the chance experiment that consists of rolling this die.
a. What are the probabilities of the six simple events? (Hint: Denote these events by O1, , O6. Then P(O1) = p, P(O2) = 2p, P(O3) = p, , P(O6) = 2p. Now use a condition on the sum of these probabili- ties to determine p.)
b. What is the probability that the number showing is an odd number? at most three?
c. Now suppose that the die is loaded so that the prob- ability of any particular simple event is proportional to the number showing on the corresponding up- turned face; that is, P(O1) = c, P(O2) = 2c, , P(O6) = 6c. What are the probabilities of the six simple events? Calculate the probabilities of Part (b) for this die.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.