- #1
amai
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Homework Statement
Suppose A is a subset of B. Using the three axioms to establish P(B)≥P(A)
Homework Equations
Axioms...
1. For any event A, P(A)[itex]\geq[/itex]0
2.P(S)=1
3.If events A1,A2... are mutually exclusive, then P([itex]\cup[/itex]Ai)=[itex]\sum[/itex]P(Ai)
The Attempt at a Solution
From the venn diagram I drew, i have...
B=A+[itex]\overline{A}[/itex]B
P(B)=P(A[itex]\cup[/itex][itex]\overline{A}[/itex]B)
P(B)=P(A)+P([itex]\overline{A}[/itex]B)
According to axiom 1, P([itex]\overline{A}[/itex]B)≥0 ... but dosen't that mean i just proved P(B)≤P(A)?