Here is the probability model for the political affiliation of a randomly chosen adult in the...

Question:

Here is the probability model for the political affiliation of a randomly chosen adult in the United States:

Political affiliation Republican Independent Democrat Other
Probability 0.22 0.45 0.31 ?

What is the probability that a randomly chosen American adult is a member of one of the two major political parties (Republicans and Democrats)?

P(Republican or Democrat) = _____

Union of Mutually Exclusive Events:

For two events A and B that are mutually exclusive, that is, they do not have any element in common, the probability of {eq}A \cup B {/eq} is calculated using the following formula:

{eq}P(A \cup B) = P(A) + P(B) {/eq}

Answer and Explanation:


Given Information:

The probability model for the political affiliation of a randomly chosen adult in the United States is given as follows:

Political affiliation Republican Independent Democrat Other
Probability 0.22 0.45 0.31 ?


The probability that a randomly chosen American adult is a member of one of the two major political parties (Republicans and Democrats) is:

{eq}\begin{align*} P(Republican\;or\;Democrat) &= P(Republican) + P(Democrat)\\ &= 0.22 + 0.31\\ &= 0.53 \end{align*} {/eq}


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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