Question 1200895
.
Given 30 questions, if the minimum passing grade is 21, what is the exact probability 
that a student passes the exam if they are guessing on each question with a 35% chance 
of guessing correctly?
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<pre>
The given problem is a Binomial distribution probability problem.


It asks about the probability of getting 21 or more successful trials in the
experiment with 30 trials and the probability of success 0.35 in each individual trial.


The formula for the probability is

    P = P(n=30; k>=21; p=0.35) = {{{sum(C[30]^i*0.35^i*(1-0.35)^(30-i),i=21,30)}}}.


The simplest way to calculate it is to use the online calculator at this site

https://stattrek.com/online-calculator/binomial.aspx


It provides nice instructions  and  a convenient input and output for all relevant options/cases.


     The resulting number is P = P(n=30, k>=21, p= 0.35) = 0.0001  (rounded).    <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).