<PRE><B>Question 1185310</B>
.
Suppose that 30% of all voters prefer Candidate A.
If 6 people are chosen at random for a poll, what is the probability that fewer than 5 of them favor Candidate A?
Probability =
(Please show your answer to 4 decimal places)
~~~~~~~~~~~~~~~~~


&lt;pre&gt;
It is a binomial distribution probability problem.

    - number of trials         n =  6;
    - number of success trials k &lt;= 4;
    - Probability of success on a single trial p = 0.30.



We need calculate  P(n=6; k&lt;=4; p=0.3).      


To facilitate calculations, I use an appropriate online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


It provides nice instructions  and  a convenient input and output for all relevant options/cases.


    P(n=6; k&lt;=4; p=0.3) = 0.989065,   or   0.9891 (rounded).       &lt;U&gt;ANSWER&lt;/U&gt;
&lt;/pre&gt;

Solved.


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If you want to see many similar &amp;nbsp;(or different) &amp;nbsp;solved problems, &amp;nbsp;look into the lessons

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson&gt;Simple and simplest probability problems on Binomial distribution&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson&gt;Typical binomial distribution probability problems&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson&gt;How to calculate Binomial probabilities with Technology (using MS Excel)&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson&gt;Solving problems on Binomial distribution with Technology (using MS Excel)&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson&gt;Solving problems on Binomial distribution with Technology (using online solver)&lt;/A&gt; 

in this site.


After reading these lessons, &amp;nbsp;you will be able to solve such problems on your own, 

which is your &amp;nbsp;PRIMARY &amp;nbsp;MAJOR &amp;nbsp;GOAL &amp;nbsp;visiting this forum &amp;nbsp;(I believe).



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