SOLUTION: 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 probab

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Question 1178073: 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?
Answer by ikleyn(53765) About Me  (Show Source):
You can put this solution on YOUR website!
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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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You can compute this probability in two different ways.


One way is  P = %28%283_blue%2F7_balls%29%29%2F%28%283_blue%2F7_balls%29%2B%282_blue%2F7_balls%29%29 = %28%283%2F7%29%29%2F%28%283%2F7%29%2B%282%2F7%29%29 = %28%283%2F7%29%29%2F%28%285%2F7%29%29 = 3%2F5 = 6%2F10 = 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%2F5_blue = 3%2F5 = 6%2F10 = 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.


Solved.