Question 1183519
.
Suppose that a quiz consists of 16 True-False questions. A student hasn't studied for the exam and will just randomly 
guesses at all answers (with True and False equally likely). How would you find the probability that the student 
will get exactly 8 answers correct? (consider up to 4 decimal places)
0.1208
0.1964
0.0229
0.8412
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<pre>
It is a typical binomial distribution probability problem.


    The number of trials is n = 16;

    The number of successful trials is  k = 8.

    The probability of the success is  {{{1/2}}}  in each individual trial (the same as the probability of the unsuccess).


The final probability is  P = {{{C[16]^8*(1/2)^16}}} = {{{((16*15*14*13*12*11*10*9)/(1*2*3*4*5*6*7*8))*(1/2^16)}}} = 0.1964  (rounded).    <U>ANSWER</U>
</pre>

Solved and explained.


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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.