Mathegoras

Probability › Events and basic probability › Events, unions and complements

Smallest p for triple intersection

University · ●●●○○ 50 pts

Let events AA, BB and CC satisfy P(A)=P(B)=P(C)=pP(A)=P(B)=P(C)=p. Find the infimum of the values of pp for which P(A∩B∩C)>0.95P(A\cap B\cap C)>0.95 holds for every possible joint distribution of AA, BB and CC. Round to four decimal places.

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linear programminginclusion-exclusion