Question
You are given the following information on Events A, B, C, and D. P(A) = .5...
You are given the following information on Events A, B, C, and D. P(A) = .5 P(B) = .3 P (C) = .20 P(A U D) = .8 P(A ∩ C) = 0.05 P (A │B) = 0.22 P (A ∩ D) = 0.25 Compute P(D). Compute P(A ∩ B). Compute P(A | C). Compute the probability of the complement of C. What does it mean to be mutually exclusive? Give an example. must show work
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Question 4 You are given the following information on Events A, B, C, and D. P(A)...
Question 4
You are given the
following information on Events A, B, C, and D.
P(A) = .5
P(B) = .3
P (C) = .20
P(A U D) = .8
P(A ∩ C) = 0.05
P (A │B) = 0.22
P (A ∩ D) = 0.25
Compute P(D).
Compute P(A ∩ B).
Compute P(A | C).
Compute the probability of the
complement of C.
What does it mean to be
mutually exclusive? Give an example.
Given the following information on Events A, B, C, and D. P(A) = 0.35 P(A U...
Given the following information on Events A, B, C, and D.
P(A) = 0.35
P(A U D) = 0.55
P(A n D) = 0.12
P(B) = 0.18
P(A I B) = 0.43
P(C) = 0.25
P(A n C) = 0.07
1.Compute P(D).
2.Compute P(A n B).
3.Compute P(A I C).
4.Compute the probability of the complement of C
5. Are events A and C independent? Explain.
Given the following information about events A, B, and C, determine which pairs of events, if...
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
1. Which of the following statements is true? A If events A and B are complements,...
1. Which of the following statements is true?
A
If events A and B are complements, then the intersection of A
and the complement of B is the sample space.
B
If events A and B are mutually exclusive, then the intersection
of A and B is the empty set.
C
If events A and B are mutually exclusive, then the union of A
and B is the sample space.
D
If events A and B are mutually exclusive, then...
What is P(C|D), given P(D|C) = 0.1, P(C) = 0.2, P(D|E) = 0.25, P(E) = 0.5,...
What is P(C|D), given P(D|C) = 0.1, P(C) = 0.2, P(D|E) = 0.25,
P(E) = 0.5, P(D|F) =0.75, and P(F) = 0.5, where E and F are
mutually exclusive and exhaustive events(either E happens or F
happens, and one of the two must happen)
Suppose that A and B are two events in a sample space S with P(B)=0.04, P(A...
Suppose that A and B are two events in a sample space
S with P(B)=0.04, P(A n B)=0.03 and P(A u B) =0.46
a) what is P(B) complement
b)what is P(A)
c)what is P( AUB) complement
d)what is P(A/B)
e)what is P(A complement n B)
f)Are two events A and B independent? justify your answer.
g) Are two events A and B mutually exclusive? Justify your
answer.
Consider events A, B, and C, with P(A) > P(B) > P(C) > 0. Events A...
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.
3) Given the events A and B, and P (A) = 0.3, P (B) = .5...
3) Given the events A and B, and P (A) = 0.3, P (B) = .5 and P
(A and B) = .1
Determine:
a) P (A∪B) b) P (A∪Bc) c) P (A / B)
Hint: make the Venn diagram
4) Given events A and B, and P (A) = 0.3, P (B) = .5 If the
events are independent, determine:
a) P (A∪B)
b) P (A∩Bc) c) P ((A∩B) c)
5) If the events are mutually exclusive, determine:
a)...
suppose events A and B are such that p(A)=0.25,P(B) =0.3 and P(B|A)= 0.5 i) compute P(AnB)...
suppose events A and B are such that p(A)=0.25,P(B)
=0.3 and P(B|A)= 0.5
i) compute P(AnB) and P(AuB)
ii) Are events A and B independent?
iii) Are events A and B mutually exclusive?
b)if P(A)=0.6, P(B)= 0.15 and P(B|A')=0.25, find the following
probabilities
I)P(B|A), P(A|B),P(AuB)
1) a. If A and B are two events, in general, P( A U B) =...
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 ___________
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