Question 1178073
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A box contains 3 blue and 4 red marbles while another box contains 2 blue and 5 red marbles. A marble drawn at random 
from one of the boxes turns out to be blue. What is the probability that it came from the first box?
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<pre>
You can compute this probability in two different ways.


One way is  P = {{{((3_blue/7_balls))/((3_blue/7_balls)+(2_blue/7_balls))}}} = {{{((3/7))/((3/7)+(2/7))}}} = {{{((3/7))/((5/7))}}} = {{{3/5}}} = {{{6/10}}} = 0.6 = 60%.


This formula is the version of the conditional probability in the full space of events.



The other way is P = {{{3_blue/5_blue}}} = {{{3/5}}} = {{{6/10}}} = 0.6 = 60%.


This formula is the version of the conditional probability in the reduced space of events.



    Both formulas are SELF-EXPLANATORY,

    and both formulas give THE SAME answer.
</pre>


Solved.