Question

A given phenomenon has three events A,B, and C whose probabilities are given as 0.32, 0.23, and 0.11 respectively

a. What are the values of P(A and B), P(B and C), and P(C and A) if all three events A, B, and C are mutually exclusive

b. What are the values of P(A and B), P(B and C), and P(C and A) if all three events A, B, and C are independent of one another

c. What are the values of P(A and B), P(B and C), and P(C and A) if all three events A, B, and C are neither independent nor mutually exclusive

e. What is the value of P(A or B) if A and B are neither mutually exclusive nor independent

Answer #1

a)

if two events are mutually exclusive, then probability of their intersection is zero.

P(A and B) = 0

P(B and C) = 0

P(C and A) =0

b)

if two events rae independent then

P( A and B) = P(A)*P(B) = 0.32*0.23=0.0736

P(B and C) = P(B)P(C) = 0.23*0.11=0.0253

P(C and A) = P(C)P(A) = 0.32*0.11=0.0352

c)

if all three events A, B, and C are neither independent nor mutually exclusive, then their probability cannot be determined from given information

d)

since, A and B are neither mutually exclusive nor independent so, P( A and B) cannot be determined from given information

hence, P(A or B) cannor be calculated

determine where events b and c are independent, mutually exclusive
both or neither. P(B) = 0.56
P(B and C) =0.12
P(C)=0.23

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 the following statements concerning the probabilities
of two events, A and B: P(A U B)= 0.85, P(A/B)= 0.54, P(B)= 0.5 .
Determine whether the events A and B are: (a) mutually exclusive,
(b) independent

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.

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.

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)...

Given the probabilities p(a)=.3 and p(b)=.2, what is the
probability of the union P(a union b) if a and b are mutually
exclusive? If a and b are independent? If b is a subset of a?
Explain your answer.

(a) Assume A and B are mutually exclusive
events, with P ( A ) = 0.36 and P ( B ) = 0.61. Find P ( A ∩ B
).
(b) Assume A and B are mutually exclusive
events, with P ( A ) = 0.34 and P ( B ) = 0.48. Find P ( A ∪ B
).
(c) Assume A and B are independent events,
with P ( A ) = 0.13 and P ( B )...

Consider two events, A and B, of a sample space such that P(A) =
P(B) = 0.7 a).Is it possible that the events A and B are mutually
exclusive? Explain. b).If the events A and B are independent, find
the probability that the two events occur together. c).If A and B
are independent, find the probability that at least one of the two
events will occur. d).Suppose P(B|A) = 0.5, in this case are A and
B independent or dependent?...

A fair coin is tossed two times, and the events A and B are
defined as shown below. Complete parts a through d.
A: {at most one tail is observed}
B: {The number of tails observed is even}
D. Find P(A), P(B), P(AUB), P( Upper A Superscript c Baseline
right parenthesis, and P(AnB) by summing the probabilities of
the appropriate sample points.
P(A)= ? (Type an integer or simplified fraction.)
Find P(B). P(B)=? (Type an integer or simplified
fraction.)
FindP(AuB)....

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