Probability of mutually exclusive events discussed

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-exclusive and independent events.

Solution Preview

First, let me provide some definitions and examples:
Mutually Exclusive Events
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Two events are mutually exclusive if they cannot occur at the same time. In another word, that means mutually exclusive is identical to being disjoint.
If two events are disjoint, then the probability of them both occurring at the same time is 0.
That is, P(A and B) = 0 ------(a)
If ...

Solution Summary

This is a proof regarding independent and mutually exclusive events.

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.

Please see the attachment for the question.
Let B and C be two events such that P(B) = 0.50 and P(C) = 0.05.
a. Determine P(B U C), given that B and C are mutuallyexclusive.
b. Determine P(B U C), given that B and C are independent.

The events A and B are mutuallyexclusive. Suppose P(A)=0.30 and P(B)=0.40. What is the probability of either A or B occurring? what is the compliment of event A? What is the meaning?

The events X and Y are mutuallyexclusive. Suppose P(X) = .05 and P(Y) =.02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?

Find the following probabilities:
a. Events A and B are mutuallyexclusiveevents defined on a common sample space. If P (A) = 0.4 and P(A or B) = 0.9, find P(B).
b. Events A and B are defined on a common sample space. If P(A) = 0.20, P(B) = 0.40, and P(A or B) = 0.56, find P(A and B)

A fair dice is rolled. What is the probability of rolling an odd number OR a number less than 3?
Also would being able to speak Chinese and being able to speak Spanish be mutuallyexclusiveevents?

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.

(a) Explain the difference between mutuallyexclusive and independent events. Can a pair of events be both mutuallyexclusive and independent? Give examples.
(b) Discuss the problems inherent in using words such as "likely," "possibly," or "probably" to convey degree of belief.
(c) One way a discrete probability distribu