Question

A sample space consists of 9 elementary outcomes e₁, e₂, ..., 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, calculate P(A ∪ B)

Answer 1

Given that: S = {e₁, e₂, e₃, e₄, e₅, e₆, e₇, e₈, e₉}

A = {e₁, e₅, e₈} and 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

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)  .....(i)

But P(B) = P(e₂) + P(e₅) + P(e₈) + P(e₉)

= 0.08 + 0.1 + 0.07 + 0.07

= 0.32

And P(A ∩ B) = {e₅, e₈}

= P(e₅) + P(e₈)

= 0.1 + 0.07

= 0.17

Putting the values in equation (i) we get

P(A ∪ B) = 0.25 + 0.32 – 0.17

= 0.40