# Statistics

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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.

• Statistics -

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?

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