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Target has a nationwide sale on Coke next weekend. Consider the following events: A. The San...

Question:

Target has a nationwide sale on Coke next weekend. Consider the following events:

A. The San Jose Target sells 200 cases of Coke

B. The San Jose Target sells more than 100 cases of Coke

C. The San Jose Target sells fewer than 50 cases of Coke

D. The Boston Target sells more than 150 cases of Coke

E. The Boston Target sells less than 75 cases of Coke

a) Identify two events that are mutually exclusive

b) Identify two events that are independent c) Identify two events that are neither mutually exclusive nor independent

Mutually Exclusive and Independent Events:

Let A and B are two events and if they are mutually exclusive, then they cannot occur at the same time. For example, while tossing a coin, both head and tail cannot occur at the same time, Both events A and B are said to be Independent, then the occurrence of one event will not affect the occurrence of the other event. For example, the event of watching a movie and eating popcorn.

Answer and Explanation:

Given that,

A. The San Jose Target sells 200 cases of Coke

B. The San Jose Target sells more than 100 cases of Coke

C. The San Jose Target sells fewer than 50 cases of Coke

D. The Boston Target sells more than 150 cases of Coke

E. The Boston Target sells less than 75 cases of Coke

a)

{eq}A {/eq} and C are mutually exclusive events. It is because both cannot occur at the same time. Few other options are,

{eq}B {/eq} and C are mutually exclusive events.

b)

{eq}A {/eq} and D are Independent events. It is because the occurrence of first event will not affect the occurrence of the other event

{eq}A {/eq} and E are mutually Independent events.

{eq}B {/eq} and D are Independent events.

{eq}B {/eq} and E are mutually Independent events.

{eq}C {/eq} and D are Independent events.

{eq}C {/eq} and E are mutually Independent events.

c)

{eq}A {/eq} and B are neither mutually exclusive nor independent.

The reason behind this is both are the same events that cannot be categorized as independent or mutually exclusive.


Learn more about this topic:

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Mutually Exclusive Events & Non-Mutually Exclusive Events

from 6th-8th Grade Math: Practice & Review

Chapter 48 / Lesson 5
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