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: 1 – (1 – P₁)(1 – P₂) 

Answer 1

Here, P(E₁) = P₁ and P(E₂) = P₂

1 – (1 – P₁)(1 – P₂) = 1 – P(E₁)'P(E₂)'

= 1 – P(E₁' ∩ E'₂)

= 1 – [1 – P(E₁ ∪ E₂)]

= P(E₁ ∪ E₂)

So, either E₁ or E₂ or both E₁ and E₂ occur.