Question 1190719
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A student is taking a​ multiple-choice exam in which each question has four choices. 
Assuming that she has no knowledge of the correct answers to any of the​ questions, 
she has decided on a strategy in which she will place four balls​ (marked A,B,C,D ​) into a box. 
She randomly selects one ball for each question and replaces the ball in the box. 
The marking on the ball will determine her answer to the question. 
There are six ​multiple-choice questions on the exam.
What is the probability that she will get at least five questions​ correct?
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<pre>
This many-words description means simple thing: for any multiple-choice question,
the answer is selected randomly among four possibilities;

so, the probability of getting a correct answer is  {{{1/4}}} = 0.25, while the probabiliy 
of getting incorrect answer is  {{{3/4}}} = 0.75  for each single multiple choice question.


And the answers to different multiple-choice questions are independent each from another.


It is a typical binomial distribution situation. The formula for the probability to get 5 or more correct answers is

    P = P(5) + P(6) = {{{C[6]^5*0.25^5*0.75^1}}} + {{{C[6]^6*0.25^6*0.75^0}}} = 

                      {{{6*0.25^5*0.75 + 0.25^6}}} = 0.004639.    <U>ANSWER</U>
</pre>

Solved.


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To see many other similar &nbsp;(and 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> 

in this site.