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}   

 List the composition of the event A ∪ B, and calculate P(A ∪ B) by addting the probabilities of elementary events.

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

A = {E₁, E₅, E₈}

B = {E₂, E₅, E₈, E₉}

Now, A ∪ B = {E₁, E₂, E₅, E₈, E₉}

∴ P(A ∪ B) = P(E₁) + P(E₂) + P(E₅) + P(E₈) + P(E₉)

                    = 0.08 + 0.08 + 0.1 + 0.07 + 0.07
 
                    = 0.40