Question 1191245
.
A Finite final consists of 30 multiple choice questions. 
If each question has 4 choices and 1 right answer, find the probability 
that a student gets an A (i.e. 27 or better) by purely guessing on each question.
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<pre>
For each individual multiple choice question of 30 multiple questions,


    the probability to guess correctly is  {{{1/4}}} = 0.25;  

    the probability to guess incorrectly is  {{{3/4}}} = 0.75.



Next,  P = P(27) + P(28) + P(29) + P(30) = use the formulas for the binomial distribution = 

         = {{{C[30]^27*0.25^27*0.75^3}}} + {{{C[30]^28*0.25^28*0.75^2}}} + {{{C[30]^29*0.25^29*0.75^1}}} + {{{C[30]^30*0.25^30*0.75^0}}} = 

         = 9.50802*10^(-14) + 3.39572*10^(-15) + 7.80626*10^(-17) + 8.67362*10^(-19) = 9.85548*10^(-14).     <U>ANSWER</U>
</pre>


Solved.


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If you want to see many similar &nbsp;(or different) &nbsp;solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> 

in this site.


After reading these lessons, &nbsp;you will be able to solve such problems on your own, 

which is your &nbsp;PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).