Question

A sample space consists of 9 elementary events E₁, E₂, E₃, ..., E₉ whose probabilities are
P(E₁) = P(E₂) = 0.08, P(E₃) = P(E₄) = P(E₅) = 0.1, P(E₆) = P(E₇) = 0.2, P(E₈) = P(E₉) = 0.07
Suppose A = {E₁, E₅, E₈}, B = {E₂, E₅, E₈, E₉}   

 Using the addition law of probability, find P(A ∪ B).

Answer 1

Let S be the sample space of the elementary events.
S = {E₁, E₂, E₃, ..., E₉}
Given:
A = {E₁, E₅, E₈}
B = {E₂, E₅, E₈, E₉}
P(E₁) = P(E₂) = 0.08, P(E₃) = P(E₄) = P(E₅) = 0.1, P(E₆) = P(E₇) = 0.2, P(E₈) = P(E₉) = 0.07

 By the addition law of probability, we have

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

                = 0.25 + 0.32 − 0.17

                = 0.40