Question

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: P₁ + P₂ – 2P₁P₂ 

Answer 1

Here, P(E₁) = P₁ and P(E₂) = P₂

P₁ + P₂ – 2P₁P₂ = P(E₁) + P(E₂) – 2P(E₁).P(E₂)

= P(E₁) + P(E₂) – 2P(E₁ ∩ E₂)

= P(E₁ ∪ E₂) – 2P(E₁ ∩ E₂)

So, either E₁ or E₂ occurs but not both.