Question

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.

Answer #1

Let A and B be events with P(A) = 0.7, P(B) = 0.9, and P
(A and B) = 0.6.
Compute P (A or B)
Are A and B mutually exclusive? Explain.

Let A and B represent events such that P(A) = 0.6, P(B) = 0.4,
and P(A ∪ B) = 0.76. Compute: (a) P(A ∩ B) (b) P(Ac ∪ B) (c) P(A ∩
Bc ) (d) Are events A and B mutually exclusive? Are they
independent? Explain by citing the definitions of mutual
exclusivity and independence.

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?...

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)...

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)

Consider the following scenario:
• Let P(C) = 0.7
• Let P(D) = 0.4
• Let P(C|D) = 0.8
Q1. P(C AND D) =
Q2. Are C and D Mutually Exclusive?
Q3 Are C and D independent events?
Q4. P(D|C) =
Round your answer to two decimal places.

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.

13.
Assume A and B are independent events with P(A)= 0.2 and P(B)= 0.3.
let C be the event that none of the events A and B occurs, let D be
the event that exactly one of the events A and B occurs. Find P(A
given D)?

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...

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