SOLUTION: Events A, B, and C are defined on sample space S. Their corresponding sets of sample points do not intersect, and their union is S. Furthermore, event B is twice as likely to occur

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Question 975260: Events A, B, and C are defined on sample space S. Their corresponding sets of sample points do not intersect, and their union is S. Furthermore, event B is twice as likely to occur as event A, and event C is twice as likely to occur as event B. Determine the probability of each of the three events.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of their probabilities equals 1 and they are mutually exclusive.
P%28A%29%2BP%28B%29%2BP%28C%29=1
P%28A%29%2B2%2AP%28A%29%2B2%2AP%28B%29=1
P%28A%29%2B2%2AP%28A%29%2B4%2AP%28A%29=1
7%2AP%28A%29=1
P%28A%29=1%2F7
Then,
P%28B%29=2%2F7
and
P%28C%29=4%2F7