# Chapter 4 - Probability - 4-3 Addition Rule - Beyond the Basics: 42

$P(A\cup B \cup C)=P(A)+P(B)+P(C)-P(A \cap B)-P(A \cap C)-P(C \cap B)+P(A \cap B \cap C).$

#### Work Step by Step

We count an element appearing in only one set once, but by this we count elements appearing in 2 sets twice, so we must subtract them, but by this we count the elements appearing in all 3 sets less times, so we must add that once. Hence the formula: $P(A\cup B \cup C)=P(A)+P(B)+P(C)-P(A \cap B)-P(A \cap C)-P(C \cap B)+P(A \cap B \cap C).$

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