Question

In: Statistics and Probability

Let S = {s1, s2, s3, s4, s5, s6} be the sample space associated with an...

Let

S = {s₁, s₂, s₃, s₄, s₅, s₆}

be the sample space associated with an experiment having the probability distribution shown in the accompanying table. If

A = {s₁, s₂}

and

B = {s₁, s₅, s₆},

find the following.

Outcome

Probability

s₁

1

3

s₂

1

7

s₃

1

6

s₄

1

6

s₅

1

21

s₆

1

7

(a)

P(A)

=

P(B)

=

(b)

P(A^C)

=

P(B^C)

=

(c)

P(A ∩ B)

=

(d)

P(A ∪ B)

=

(e)

P(A^C ∩ B^C)

=

(f)

P(A^C ∪ B^C)

=

Expert Solution

s1	1/3
s2	1/7
s3	1/6
s4	1/6
s5	1/21
s6	1/7

A =	{s1, s2}	3456
B =	{s1, s5, s6}	234

a) P(A) =	P(s1) + P(s2) =	1/3 + 1/7 =	10/21
b) P(B) =	P(s1) + P(s5) +P(s6) =	1/3 + 1/21 + 1/7 =	11/21
c) P(Ac) =	1 - P(A)	1 - 10/21 =	11/21
d) P(Bc) =	1 - P(B)	1 - 11/21 =	10/21
e) P(A and B) =	P(s1)	1/3	1/3
f) P(A or B) =	P(s1) + P(s2) + P(s5) + P(s6)	1/3 + 1/7+1/21 + 1/7 = 14/21	2/3
g) P(Ac and Bc) =	P(A or B)c = 1 - P(A or B)	1 - 2/3	1/3
h) P(Ac or Bc) =	P(A and B)c = 1 - P(A and B)	1 - 1/3	2/3

orchestra answered 2 years ago

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