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}   

 Compute P(A), P(B) and 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

P(A) = P(E₁) + P(E₅) + P(E₈) = 0.08 + 0.1 + 0.07 = 0.25  

P(B) = P(E₂) + P(E₅) + P(E₈) + P(E₉) = 0.08 + 0.1 + 0.07 + 0.07 = 0.32

Now, A ∩ B = {E₅, E₈}

∴ P(A ∩ B) = P(E₅) + P(E₈) = 0.1 + 0.07 = 0.17