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Chapter 4: Problem 42

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

Short Answer

Expert verified
Mutually exclusive events are events that cannot happen simultaneously - if one occurs, the other cannot. As an example, flipping a coin can result in either heads or tails, but not both - these are mutually exclusive events. In contrast, mutually non-exclusive events can occur together. For instance, when drawing a card, it being a 'heart' and it being a 'face card' are not mutually exclusive, as there can be cards like 'King of Hearts' which satisfy both conditions.

Step by step solution

01

Define Mutually Exclusive Events

In probability, two events are said to be mutually exclusive if they cannot happen at the same time. In other words, the occurrence of one event excludes the occurrence of the other.
02

Example of Mutually Exclusive Events

For instance, consider flipping a fair coin. It can either land on heads or tails. However, it cannot land on both heads and tails at the same time. So, the events 'landing on heads' and 'landing on tails' are mutually exclusive.
03

Define Mutually Non-Exclusive Events

By contrast, mutually non-exclusive events can happen at the same time. These are events which do not prevent each other from happening.
04

Example of Mutually Non-Exclusive Events

Let's consider a deck of cards. Drawing a card that is a 'heart' and drawing a card that is a 'face card' are not mutually exclusive. These two events can occur simultaneously. For example, a 'King of Hearts' is both a heart and a face card.

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Most popular questions from this chapter

A company hired 30 new college graduates last week. Of these, 16 are female and 11 are business majors. Of the 16 females, 9 are business majors. Are the events "female" and "business major" independ. ent? Are they mutually exclusive? Explain why or why not.

Find the joint probability of \(A\) and \(B\) for the following. a. \(P(A)=.40\) and \(P(B \mid A)=.25\) b. \(P(B)=.65\) and \(P(A \mid B)=.36\)

Find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.58, \quad P(B)=.66\), and \(P(A\) and \(B)=.57\) b. \(P(A)=.72, \quad P(B)=.42\), and \(P(A\) and \(B)=.39\)

Given that \(A\) and \(B\) are two independent events, find their joint probability for the following. a. \(P(A)=.20\) and \(P(B)=.76\) b. \(P(A)=.57\) and \(P(B)=.32\)

Suppose that \(20 \%\) of all adults in a small town live alone, and \(8 \%\) of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?
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