Events A, B, and C are defines on sample space S. Their corresponding sets of sample points do not intersect and their union is S. Further, 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 these three events.

Question

Events A, B, and C are defines on sample space S.  Their corresponding sets of sample points do not intersect and their union is S.  Further, 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 these three events.

MathMate · Answer

Given: S=A∪B∪C=sample space ∅=A∩B ∅=B∩C ∅=C∩A P(A)=2P(B) P(B)=2P(C) Therefore P(S)=1 P(A)+P(B)+P(C)=1 2P(B)+2P(C)+P(C)=1 4P(C)+2P(C)+P(C)=1 7P(C)=1 P(C)=1/7 Can you find the rest?