Question

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]

Answer 1

Answer:

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