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

Question 804647: 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. (Give your answers as fractions.)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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. (Give your answers as fractions.)
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A + B + C = S
B = 2A
C = 2B = 4A
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Note: The probabilities must add up to 1.
a + 2a + 4 = 1
7a = 1
P(A) = 1/7
P(B) = 2/7
P(C) = 4/7
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Cheers,
Stan H.
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