Question
I really need help on this question can someone plz help me.
If P(A)=2/11,P(B)=3/11,and P(C)=4/11, what can you say about P(A or B or C) when P(A and B and C) = 0?
If P(A)=2/11,P(B)=3/11,and P(C)=4/11, what can you say about P(A or B or C) when P(A and B and C) = 0?
Answers
MathMate
P(A∪B∪C) = P(A)+P(B)+P(C)
if and only if P(A∩B)=0 ∩ P(B∩C)=0 ∩ P(C∩A)=0
Therefore, when P(A∩B∩C)=0, we can conclude that:
P(A∪B∪C) ≤ P(A)+P(B)+P(C)
or
P(A∪B∪C)
= P(A)+P(B)+P(C) - (P(A∩B) + P(B∩C) + P(C∩A))
if and only if P(A∩B)=0 ∩ P(B∩C)=0 ∩ P(C∩A)=0
Therefore, when P(A∩B∩C)=0, we can conclude that:
P(A∪B∪C) ≤ P(A)+P(B)+P(C)
or
P(A∪B∪C)
= P(A)+P(B)+P(C) - (P(A∩B) + P(B∩C) + P(C∩A))