Question 1155656
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 A stack of playing cards contains 4 jacks, 5 queens, 3 kings, and 3 aces. Two cards will be randomly selected from the stack. 
What is the probability that a queen is chosen and replaced, and then a queen is chosen again?
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The formulation of the problem in your post is INCORRECT.


The correct formulation is THIS :


<pre>
     A stack of playing cards contains 4 jacks, 5 queens, 3 kings, and 3 aces. Two cards are randomly selected  

     from the stack with replacement. What is the probability that a queen is chosen, and then a queen is chosen again?
</pre>

Do you see the difference ?


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<pre>
The solution and the answer are  P = {{{(5/15)*(5/15)}}} = {{{(1/3)*(1/3)}}} = {{{1/9}}}.


Here 15 = 4 + 5 + 3 + 3 is the total number of playing cards in the stack.
</pre>