Question

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 ___________

Answer #1

1)

a. If A and B are two events, in general, P( A U B) = P(A) + P(B) – P(A ∩ B)

(by using definition of union of two events in general.)

b. if A and B are two mutually exclusive events, P( A U B)= P(A) + P(B)

Explanation:

For two mutually exclusive events A and B, we know that P(A ∩ B) = 0, so

P( A U B) = P(A) + P(B) – P(A ∩ B) = P(A) + P(B) – 0 = P(A) + P(B)

c. If A and B are two events, in general P( A **∩**
B) = P(A) + P(B) – P(A U B)

(by using definition of union and intersection of two events in general)

d. If A and B are two independent events, P(A **∩**
B)= P(A)*P(B), since A and B being independent means

(by using definition of intersection of two independent events A and B)

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

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.

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...

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 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?...

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.

Q1) If A and B are mutually exclusive events and P(A) = 0.2 and
P(B) = 0.7, then P(A and B) is
A) .7600
B) .9000
C) .0000
D) .1400
Q2) If A and B are two independent events with P(A) = 0.1535 and
P(B) = 0.6429, then P(A ∪ B) is
A) 0.7964
B) 0.0987
C) 0.3070
D) 0.6977

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 ?

Suppose A and B are two events such that 0< P(A)<1 and
0< P(B)<1. Show that if P(A|B) =P(A|Bc), then A and B are not
mutually exclusive.

(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 )...

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