Let E and F be non-zero-probability events. If E and F are mutually-exclusive, can they also be independent? Explain the answer, and also prove it algebraically using the definitions of mutually-exclusiveandindependentevents.

Let A and B be two events such that P(A) = 0.32 and P(B) = 0.41.
a. Determine the probability of the union of A and B given that A and B are mutuallyexclusive.
b. Determine the probability of the union of A and B given that A and B are independent.

Probability of union: Basic
Let A and C be two events such that P (A) = 0.22 and P (C) = 0.54.
(a) Determine P (AUC), given that A and C are independent.
(b) Determine P (AUC), given that A and C are mutuallyexclusive.
Do not round your responses.
Please see attached file.

Independent projects are projects whose cash flows are independent of one another.
MutuallyExclusive projects are projects where only one can be accepted.
Can you provide some examples from your experience of each type of decision?

Select the correct answer and explain briefly why
1. Two mutually exclusive events having positive probabilities are ______________ dependent.
A. Always
B. Sometimes
C. Never
They are necessarily dependent because the occurrence of one (seriously) affects the probability of the other (makes it zero).
2. If P(A)>0 a

Give an example of three events that would be mutuallyexclusive. Are these events also exhaustive? Then, give an example of three events that would be exhaustive. Are these exhaustive events also mutuallyexclusive? Fully explain your response.

See the attached file.
1) Let A and B be two events.
a) If the events A and B are mutuallyexclusive, are A and B always independent? If the answer is no, can they ever be independent? Explain
b) If A is a subset of B, can A and B ever be independentevents? Explain
2) Flip an unbiased coin five independent times. Compute

Can a mutuallyexclusiveevents be independent at the same time?
I know that Binomial distribution is not another representation of a discrete probability distribution, but an example. Can you give two other ways of representing a discrete probability distribution? Or Can a pair of events be both mutuallyexclusiveand indepe

Please helps with the following problem.
1.) The special rule of addition is used to combine
a.) events that total more than one
b.) mutuallyexclusiveevents
c.) events based on subjective probabilities
d.) independentevents
2) Events are independent if
a.) we can count the possible outcomes
b.) the pro