Question

Mutually exclusive events also independent.

True or False?

Answer #1

**Answer : False**

**Mutually exclusive events cannot be
independent.**

If an event is mutually exclusive, occurence of one event excludes the other. That means two events cannot occur at the same time.

Eg : Tossing a coin means you can get either head or tail but can't get both at the same time.

But in the case of independent events, occurence of one event does not affect the occurrence of other.

Eg : Tossing two coins means you can get either of the two possibilities in both coins.

And hence mutually exclusive events cannot be independent. They are dependent as one event affects the other.

Discuss the concepts of mutually exclusive events and
independent events. List several examples of each type of event
from everyday life.
If A and B are mutually exclusive events, does it follow that A
and B cannot be independent events? Give an example to
demonstrate your answer. Hint: Discuss an election where
only one person can win the election. Let A be the event that party
A's candidate wins, and let B be the event that party B's candidate
wins....

True or False, explain. If false, give counter example.
a) if events A and B disjoint then A and B independent.
b) if events A and B independent then A and B disjoint.
c) It is impossible for events A and B to be both mutually
exclusive and independent.

Prove: If A and B are mutually exclusive, and A and B are also
independent, then either A or B has probability zero.

What is meant by two mutually exclusive events? Give one example
of two mutually exclusive events and another example of two
mutually nonexclusive events.

a. The following events are mutually exclusive: Living in
California and watching American Idol. True or
False
b. The number of patients seen by an outpatient practice is an
example of a discrete random variable. True or
False
c.The law of large numbers states that as the number of times an
event experiment is conducted increases, the likelihood of the
actual probability of an event approaching the theoretical
probability decreases. True or False
d. Measuring the time it takes for...

(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 )...

determine where events b and c are independent, mutually exclusive
both or neither. P(B) = 0.56
P(B and C) =0.12
P(C)=0.23

Alternatives are usually of two types: mutually exclusive and
independent. Explain the meaning of mutually exclusive
alternatives.

A if two events are mutually exclusive, then their interexction
probability will be freater than zero
B For the standard normal probaility distribution, the area to
the left of the mean is greater than 0.5
C as the number of degrees of freedom in a t distribution
increases, the difference between the T distribution and the
standard normal distribution becomes smaller
This 3 statement is true or false

independent versus mutually exclusive projects?

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