Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E4} B = {E2, E3} C = {E2, E4, E5}. (a) Find P(A), P(B), and P(C). P(A) = P(B) = P(C) = (b) Find P(A ∪ B). P(A ∪ B) = Are A and B mutually exclusive? They mutually exclusive. (c) Find AC. (Enter your answer in set notation.) AC = Find CC. (Enter your answer in set notation.) CC = Find P(AC) and P(CC). P(AC) = P(CC) = (d) Find A ∪ BC. (Enter your answer in set notation.) A ∪ BC = Find P(A ∪ BC). P(A ∪ BC) = (e) Find P(B ∪ C). P(B ∪ C) =
Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E4} B = {E2, E3} C = {E2, E4, E5}. (a) Find P(A), P(B), and P(C). P(A) = P(B) = P(C) = (b) Find P(A ∪ B). P(A ∪ B) = Are A and B mutually exclusive? They mutually exclusive. (c) Find AC. (Enter your answer in set notation.) AC = Find CC. (Enter your answer in set notation.) CC = Find P(AC) and P(CC). P(AC) = P(CC) = (d) Find A ∪ BC. (Enter your answer in set notation.) A ∪ BC = Find P(A ∪ BC). P(A ∪ BC) = (e) Find P(B ∪ C). P(B ∪ C) =
Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E4} B = {E2, E3} C = {E2, E4, E5}. (a) Find P(A), P(B), and P(C). P(A) = P(B) = P(C) = (b) Find P(A ∪ B). P(A ∪ B) = Are A and B mutually exclusive? They mutually exclusive. (c) Find AC. (Enter your answer in set notation.) AC = Find CC. (Enter your answer in set notation.) CC = Find P(AC) and P(CC). P(AC) = P(CC) = (d) Find A ∪ BC. (Enter your answer in set notation.) A ∪ BC = Find P(A ∪ BC). P(A ∪ BC) = (e) Find P(B ∪ C). P(B ∪ C) =
Suppose that we have a sample space with five equally likely experimental outcomes:
E1, E2, E3, E4, E5.
Let
A
=
{E1, E4}
B
=
{E2, E3}
C
=
{E2, E4, E5}.
(a)
Find
P(A), P(B), and P(C).
P(A)
=
P(B)
=
P(C)
=
(b)
Find
P(A ∪ B).
P(A ∪ B)
=
Are A and B mutually exclusive?
They mutually exclusive.
(c)
Find
AC.
(Enter your answer in set notation.)
AC =
Find
CC.
(Enter your answer in set notation.)
CC =
Find
P(AC)
and
P(CC).
P(AC)
=
P(CC)
=
(d)
Find
A ∪ BC.
(Enter your answer in set notation.)
A ∪ BC =
Find
P(A ∪ BC).
P(A ∪ BC)
=
(e)
Find
P(B ∪ C).
P(B ∪ C)
=
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
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