Question 1205065
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A deck of cards is shuffled well. The cards are dealt one-by-one until the two of hearts appears. 
Find the probability that exactly one king, queen, and jack appear before the two of hearts.
a) 1/11 b) 1/22 ​c) 1/33 ​d) 1/44
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        As the problem is worded, it is AMBIGOUS. 
        To avoid ambiguity, it should be re-formulated this way:


                    Find the probability that exactly one king, queen, and jack appear 
                    {{{highlight(IMMEDIATELY)}}} before the two of hearts.


        Agree that these are two different formulations describing two completely different situations.



<pre>
The probability that 1-st dealt card is a king  is {{{4/52}}}.

The probability that 2-nd dealt card is a queen is {{{4/51}}}.

The probability that 3-rd dealt card is a jack  is {{{4/50}}}.

The probability that first three dealt cards are a king, a queen and a jack in any order is

    {{{3!*(4/52)*(4/51)*(4/50)}}} = {{{6*(4/52)*(4/51)*(4/50)}}}.



The probability that the next dealt card is the two of heard is {{{1/49}}}.



So, the probability to have four first cards as described is


   {{{6 * (4/52) * (4/51) * (4/50) * (1/49) }}} = {{{(6*4*4*4*1)/(52*51*50*49)}}} = 

      = {{{384/6497400}}} = {{{16/270725}}} = 5.91006E-05.    <U>ANSWER</U>


There is nothing in common with your list of possible answers.
</pre>

Solved.