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Chapter 2: Q. 2.11 (page 53)

If P(E)=.9andP(F)=.8, show thatP(EF)鈮�.7.In general, prove Bonferroni鈥檚 inequality, namelyP(EF)鈮�P(E)+P(F)鈭�1.

Short Answer

Expert verified

Therefore,

TransformP(E鈭�F)鈮�1.

Use the proven inequality to getP(EF)鈮�0.7.

Step by step solution

01

Given Information.

Given P(E)=.9andP(F)=.8.

02

Explanation.

For any eventsE,F

P(E)+P(F)-1鈮�P(EF)

This is because:

P(E鈭�F)鈮�1P(E鈭�F)=P(E)+P(F)-P(EF)P(E)+P(F)-P(EF)鈮�1P(E)+P(F)-1鈮�P(EF)

So if P(E)=0.9andP(F)=0.8.

P(EF)鈮�P(E)+P(F)-1=0.9+0.8-1=0.7

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