Basic Relationships of Probability: P(A B) = P(A) + P(B) P(A B) P(A B) = P(A) + P(B) if A and

Basic Relationships of Probability:

P(A ꓴ B) = P(A) + P(B) – P(A ꓵ B)

P(A ꓴ B) = P(A) + P(B)     if A and B are mutually exclusive

P(A ꓵ B) = 0 if A and B are mutually exclusive

P(A^C) = 1 – P(A)

P(A | B) = P(A) if A and B are independent

Suppose we have a sample space S = {E₁, E₂, E₃, E₄, E₅, E₆} with probabilities P(E₁) = 0.05, P(E₂) = 0.20, P(E₃) = 0.20, P(E₄) = 0.25, P(E₅) = 0.15, P(E₆) = 0.10, and P(E₇) = 0.05. Consider the following events with their corresponding set of sample points:

A = {E₁, E₄, E₆}

B = {E₂, E₄, E₇}

C = {E₂, E₃, E₅, E₇} 

Find the probabilities: P(A), P(B) and P(C).

Find the set of sample points of events A ꓴ B (this is a list of sample points { … }.) and find

P(A ꓴ B)?

Find the set of sample points of A ꓵ B and find P(A ꓵ B).

Now use the formula P(A ꓴ B) = P(A) + P(B) – (A ꓵ B) to confirm your answer from part (b).

Are events A and C mutually exclusive?

Find B^C and P(B^C)

Calculate P(A | B) and P(B | A). Are they the same?

Are events A and B independent?