If A1, A2, A3, ..., An are any n events, then

Engineering

Mathematics

Basic Definitions Related to Probability

Question

If A₁, A₂, A₃, ..., A_n are any n events, then

P(A₁⋃A₂⋃...⋃A_n) = P(A₁) + P(A₂) +...+ P(A_n)

None of these

P(A₁⋃A₂⋃...⋃A_n) > P(A₁) + P(A₂) +...+ P(A_n)

P(A₁⋃A₂⋃...⋃A_n) ≤ P(A₁) + P(A₂) +...+ P(A_n)

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For any two events A and B, we have

P(A⋃B) = P(A) + P(B) − P(A∩B) ⇒ P(A⋃B) ≤ P(A) + P(B)
Using principle of mathematical induction it can be easily established that

$P (\cup_{i = 1}^{n} A_{i}) \leq \sum_{i = 1}^{n} P (A_{i})$