Question

- 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.

Answer #1

A and B are mutually exclusive and exhaustive , so :

P[A]+P[B] = 1

a) C and B can be mutually exclusive , if C is subset of A .

b)

**If (a) is true , that is C is subset of A**

B and C will be independent if :

Now , as , A and B are mutually exclusive and C is subset of A , so C and B are also mutually exclusive .

But P[B] >0 and P[C] > 0

so,

so, B and C can't be independent .

**if (a) is not true , that is C is subset of
B**

Then obviously

so, B and C cannot be independent .

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 ?

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, B, and C are MUTUALLY INDEPENDENT and P(a) =
1/4, P(B) = 1/3, and P(C) =1/2 and N denotes the total number of
events among A, B, C, that occur
(a) Draw a venn diagram
(b) What is the E(N)
(c) What is E(N^2)
(d) What is Cov(Ia,N)
(e) Find P(N <= 2 | C)
Thank you!

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?...

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...

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...

Let A and B be events with P (A)= 0.3 and P (B)=0.7, and P (A or
B)=0.9. (a) Compute . (b) Are and mutually exclusive? Explain. (c)
Are and independent? Explain.

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.

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

(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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