Question

The events X and Y are mutually exclusive. suppose P(X) = 0.18 and P(Y) = 0.16

What is the probability of either occurring?

What is the probability that neither will happen?

Answer #1

Solution:

Given,

The events X and Y are mutually exclusive i.e. P (X and Y) = 0

P(X) = 0.18

P(Y) = 0.16

1. Probability of either occurring.

P (Either X **or** Y) = P(X) + P(Y) - P (X
**and** Y)

P (Either X **or** Y) = 0.18 + 0.16 - 0

P (Either X **or** Y) = 0.34

Hence, 0.34 is the probability of either occurring.

2. Probability of neither occurring.

P (Neither X **nor** Y) = 1 - P (Either X
**or** Y)

P (Neither X **nor** Y) = 1 - 0.34

P (Neither X **nor** Y) = 0.66

Hence, 0.66 is the probability of neither occurring.

Events Y and Z are mutually exclusive. P(Y) =
5/8, P(Z) = 1/16 . What is the probability that either
Y
or Z will occur? Show your work.

Events A and B are mutually exclusive. Suppose event A occurs
with probability 0.82 and event B occurs with probability 0.03.
Compute the probability that A occurs or B does not occur (or
both). Compute the probability that either A occurs without B
occurring or A and B both occur.

Events A and B are mutually exclusive. Suppose event A occurs
with probability 0.57 and event B occurs with probability 0.12.
Compute the probability that A does not occur or B does not occur
(or both). Compute the probability that neither the event A nor the
event B occurs. (If necessary, consult a list of formulas.)

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

Q1) If A and B are mutually exclusive events and P(A) = 0.2 and
P(B) = 0.7, then P(A and B) is
A) .7600
B) .9000
C) .0000
D) .1400
Q2) If A and B are two independent events with P(A) = 0.1535 and
P(B) = 0.6429, then P(A ∪ B) is
A) 0.7964
B) 0.0987
C) 0.3070
D) 0.6977

Does the compound event consist of two mutually exclusive
events? Two dice are rolled. The sum of the dice is a 4 or a 9. .
Compute the probability of the compound event occurring.

Decide whether the events are mutually
exclusive.
Being one of the tallest people in the United States and being
under 4 feet tall
Are the events mutually exclusive?
A. Yes. In order for one of the events to occur, both events
must occur simultaneously.
B. Yes. It is not possible for both events to occur
simultaneously.
C.No. Neither event can ever occur.
D: No. It is possible for both events to occur
simultaneously.

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....

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?...

Suppose A and B are two events such that 0< P(A)<1 and
0< P(B)<1. Show that if P(A|B) =P(A|Bc), then A and B are not
mutually exclusive.

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