Independent or mutually exclusive

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Let $P(A)=0,4$ and $P(B)=0,5$. For what value of $P(A\cap B)$ are the events independent? For what value are they mutually exclusive?

Solution

Two events are independent when the probability of the intersection is the product of the probabilities: $P(A\cap B) = P(A)\,P(B) = 0,4\cdot 0,5 = \boxed{0,2}$ Two events are mutually exclusive (disjoint) when they cannot occur together, i.e. their intersection is empty: $P(A\cap B) = \boxed{0}$ Note that, with these non-zero probabilities, the events cannot be independent and mutually exclusive at the same time.

Links

Topics: Probabilita
Concepts: Eventi incompatibili · Eventi indipendenti
Skills: Calcolo probabilita
Exercise type: Problema probabilita