Question 1196684
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1)  There are 4 golden coins and 8 iron coins in a bag. You select one coin from the bag, 
if it is a golden coin, you keep it; but if it is an iron coin, you put it back in the bag. 
Find the probability of earning exactly 2 golden coins after:  
a)  Two consecutive selections
b)  Three consecutive selections 
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            I read,  interpret and solve part  (b)  in other way  (differently)  than tutor @greenestamps.


                                   Part  (b)



<pre>
There are 3 paths that lead to earning 2 golden coins after three selections:

    (Golden, Golden, Iron);  (Golden; Iron; Golden),  and  (Iron, Golden, Golden).


The partial/individual probabilities are

    P(GGI) = {{{(4/12)*(3/11)*(8/10)}}} = {{{(4*3*8)/(12*11*10)}}} = 0.072727273  (rounded);

    P(GIG) = {{{(4/12)*(8/11)*(3/11)}}} = {{{(4*8*3)/(12*11*11)}}} = 0.066115702  (rounded);

    P(IGG) = {{{(8/12)*(4/12)*(3/11)}}} = {{{(8*4*3)/(12*12*11)}}} = 0.060606061  (rounded).


Next, I calculate the sum of the found partial probabilities and get the <U>ANSWER</U>:  

    P(to earn 2 golden coins after 3 selections) = 0.072727273 + 0.066115702 + 0.060606061 = 0.199449 (rounded).
</pre>

Solved.