# Suppose that a six-sided die i

Suppose that a six-sided die is weighted so that any even-numbered face is four times as likely to land face up as any odd-numbered face.
(a)
What are the probabilities of the six simple events? (Hint: Denote these events by O1,   , O6. Then P(O1) = p, P(O2) = 4p, P(O3) = p, P(O6)= 4p.
Now use a condition on the sum of these probabilities to determine p. Answer as an exact fraction or round your answers to three decimal places.)
P(O1)=
P(O2)=
P(O3)=
P(O4)=
P(O5)=
P(O6)=
(b)
What is the probability that the number showing is an even number? (Give the answer to three decimal places.)

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