A space S is defined as S = {1, 3, 5, 7, 9, 11}, and three subsets as A = {1, 3, 5}, B = {7, 9, 11}, C = {1, 3, 9, 11}. Assume that each element has probability 1/6. Find the following probabilities:

(a) Pr (A)

(b) Pr (B)

(c) Pr (C)

(d) Pr (A ∪ B)

(e) Pr (A ∪ C)

(f) Pr[ (A - C) ∪ B]

a) 0.5

b) 0.5

c) 0.67

d) 1

e) 0.83

f) 0.67

Step-by-step explanation:

a)

P (A) = n (A) / n (S)

n (A) = number of outcomes in event A=3

n (S) = Total number of outcome of an experiment=6

P (A) = 3/6=1/2=0.5

b)

P (B) = n (B) / n (S)

n (B) = number of outcomes in event B=3

P (B) = 3/6=1/2=0.5

c)

P (C) = n (C) / n (S)

n (C) = number of outcomes in event C=4

P (C) = 4/6=2/3=0.67

d)

A∪B = {1,3,5} ∪ {7,9,11}={1,3,5,7,9,11}

P (A∪B) = n (A∪B) / n (S) = 6/6=1

e)

A∪C={1,3,5}∪{1,3,9,11}={1,3,5,9,11}

P (A∪C) = n (A∪C) / n (S) = 5/6=0.83

f)

A-C={1,3,5}-{1,3,9,11}={5}

(A-C) ∪B={5}∪{7,9,11}={5,7,9,11}

P ((A-C) ∪B) = n ((A-C) ∪B) / n (S) = 4/6=2/3=0.67