<PRE><B>Question 1194549</B>
.



&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;It is a standard binomial distribution problem.



&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;Part &amp;nbsp;(&amp;nbsp;a&amp;nbsp;)



&lt;pre&gt;
The number of trials is n=25;  the number of successful trials is 15; 
the probability of success for each single individual trial is p = 0.75.


     The formula to calculate the probability is


         P = P(n=25; k=15; p=0.75) = {{{C[25]^15*0.75^15*(1-0.75)^(25-15)}}} = {{{3268760*0.75^15*0.25^10}}}.


         The resulting number is P = 0.041658351 = 0.04166  (rounded).    &lt;U&gt;ANSWER&lt;/U&gt;
&lt;/pre&gt;

Part &amp;nbsp;(a) &amp;nbsp;is solved.


Solve part &amp;nbsp;(b) &amp;nbsp;in the same way.


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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).



</PRE>