Question 648024
A student has to sit for an examination consisting of 3 questions selected randomly from a list of 100 questions. 
To pass, he should answer all the three questions. What is the probability that the student will pass the examination, 
if he knows the {{{highlight(cross(answer))}}} <U>answers</U> to 90 questions on the list.
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The problem can be solved in two ways.
I will present both the ways below.


<pre>
                   <B><U>First, simple way</U></B>


The probability correctly answer 1st question is  {{{90/100}}}.

The probability correctly answer 2nd question is  {{{89/99}}}  (if the 1st is just answered correctly).

The probability correctly answer 3rd question is  {{{88/98}}}  (if both the 1st and the 2nd questions are just answered correctly).


The probability to pass the exam is

    P = {{{(90/100)*(89/99)*(88/98)}}} = 0.7265  (rounded).    <<<---===  <U>ANSWER</U>


         <B><U>Second, slightly more complicated way</U></B>


The number of all triple questions taken from 100 questions is  C(100,3) = 161700 combinations.

The number of all "correct" triples questions taken from 90 questions is  C(90,3) = 117480.

The probability under the problem's question is the ratio

    P = {{{favorable/total) = {{{C90,3)/C100,3)}}} = {{{117480/161700}}} = 0.7265  (rounded).


You get the same answer.
</pre>

Thus you have two solutions from my post for your better understanding.