Question

Given two events A and B, is it possible for these events to be:

1. Both mutually exclusive and collectively exhaustive?

2. Both mutually exclusive and independent?

3. Both mutually exclusive and A ⊆ B ?

4. Both collectively exhaustive and A ⊆ B ?

Answer #1

Two events A and B are mutually exclusive when , collectively exhaustive when and independent

Given two events A and B, the possible events are :

ans->

1. Both mutually exclusive and collectively exhaustive

2. Both mutually exclusive and independent ( only possible when P(A) = P(B) = 0,

4. Both collectively exhaustive and A ⊆ B ( possible when B is the universal set)

Consider events A, B, and C, with P(A) > P(B) > P(C) >
0. Events A and B are mutually exclusive and collectively
exhaustive. Events A and C are independent.
(a) Can events C and B be mutually exclusive? Explain your
reasoning. (Hint: You might find it helpful to draw a Venn
diagram.)
(b) Are events B and C independent?
Explain your reasoning.

1)Explain why probability is important in decision making.
2) Think of the following two possibilities:
A) You have never caught a fish
B) You have caught a fish longer than 12 inches
...Which of the following is true: 1) A & B are mutually
exclusive and collectively exhaustive
2) A & B are mutually exclusive but not collectively
exhaustive
3) A & B are not mutually exclusive but are collectively
exhaustive
4) A & B are not mutually exclusive nor...

Let A and B be two events such that P(A) = 0.8, P(B) = 0.6 and
P(A B) = 0.4. Which statement is correct?
a.
None of these statements are correct.
b.
Events A and B are independent.
c.
Events A and B are mutually exclusive (disjoint).
d.
Events A and B are both mutually exclusive and independent.
e.
Events A and B are the entire sample space.

State, with evidence, whether each of the following
statements is true or false:
a. The probability of the union of two events cannot
be less than the probability of their intersection.
b. The probability of the union of two events cannot
be more than the sum of their individual
probabilities.
c. The probability of the intersection of two events
cannot be greater than either of their individual
probabilities.
d. An event and its complement are mutually exclusive.
e. The individual...

1) a. If A and B are two events, in general, P( A U B) =
b. if A and B are two mutually exclusive events, P( A U B)=
c. If A and B are two events, in general P( A ∩
B)=
d. If A and B are two independent events, P(A ∩
B)= , since A and B being independent means ___________

Given the following information about events A, B, and C,
determine which pairs of events, if any, are independent and which
pairs are mutually exclusive.
P(A)=0.73
P(B)=0.08
P(C)=0.17
P(B|A)=0.73
P(C|B)=0.17
P(A|C)=0.17
Select all that apply:
A and C are mutually exclusive
A and B are independent
B and C are mutually exclusive
A and C are independent
A and B are mutually exclusive
B and C are independent

Consider two events A and B from the same sample space S.
Which of the following statements is not true:
a) If A and B are independent, then P left parenthesis A right
parenthesis equals P left parenthesis right enclose A B right
parenthesis
b) If A and B are mutually exclusive events, then P left
parenthesis A union B right parenthesis equals P left parenthesis A
right parenthesis plus P left parenthesis B right parenthesis
c) If A and...

1. A and B are independent events, and P(A) = 0.5 and P(B) =
0.8.
Find P(A and B)
2. Suppose that P(A) = 0.3, P(B) = 0.4, and
P(A and B) = 0.12.
a. What is P(A|B)?
b. What is P(B|A)?
c. Are A and B independent
3) Describe in your own words why the following statements
are
correct.
a. Two events cannot be independent if they are already
known to be mutually exclusive
b. Two events cannot be...

16. Two events are considered to be ________ if they cannot
occur at the same time during the experiment.
mutually exclusive
collectively exhaustive
independent
dependent
12.
The daily high temperature in Philadelphia over an eight-day
period is shown below.
69
77
70
81
84
86
69
70
The median for this data set is ________.
69
70
73.5
77
10.
Use a ________ chart if you want to compare the relative sizes
of the classes in a frequency distribution and...

4). Give examples of events, A and B, that are
independent. Answer using sentences.
A =
B =
5) Give examples of events, C and D, that are mutually
exclusive.
C =
D =
6). Given P(A ) = .5 and P( B ) = .2 and P( A and B ) = .1, find
P ( B/A ).
7) Given P(A ) = .4, P ( B ) = .3 and A and B are Mutually
exclusive, find
P
(A...

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