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In a bag there are 3 orange marbles, 4 blue marbles and 5 green marbles. 4. What is the probability of blindly reaching in the bag and pulling out a not-blue and not-orange marble?.

I know the answer is 8/12 or 2/3. My question is why this problem can't be solve using this way:

not blue = green (5) + orange (3) = 8, the probability is 8/12 not orange = green (5) + blue (4) = 9, the probability is 9/12

then the probability of blindly reaching in the bag and pulling out a not-blue and not-orange marble is (8/12 + 9/12) - (8/12 x 9/12) = 11/12.

I would be grateful for the explanations.

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  • $\begingroup$ After you take out the first marble, won't the individual probabilities change for each colour? $\endgroup$
    – Zeeshan Ahmad
    Sep 17, 2017 at 18:29
  • $\begingroup$ still beyond my reasoning. any suggestion (pdfs or webs) on what to read to improve my reasoning on basic probability? thanks $\endgroup$
    – jonforall
    Sep 17, 2017 at 18:39
  • $\begingroup$ What he means to say is that after you take out the first marble, there are now 11 in the bag, so the probabilities change when you take out the 2nd marble. $\endgroup$
    – DaveNine
    Sep 17, 2017 at 21:54
  • $\begingroup$ I think the problem may be poorly stated by OP.. the way you have it stated makes it sound like you're choosing two marbles, however in the answer below, it is assumed you're choosing one marble that is neither blue nor orange. I can see it being interpreted both ways. $\endgroup$
    – DaveNine
    Sep 17, 2017 at 22:04
  • $\begingroup$ I mean I just choose one marble $\endgroup$
    – jonforall
    Sep 17, 2017 at 22:35

1 Answer 1

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We have $12$ marbles total. We know that the probability of picking a not-blue marble is $2/3$ and the probability of picking not-orange marble is $3/4$. Now since we are looking at the case where we don't pick an orange or blue marble then the outcomes desired are picking a green marble. In probability we have this equation:

$$\frac{\text{outcomes desired}}{\text{total possible outcomes}}$$

Hopefully this helps guide you to your answer.

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  • $\begingroup$ Doesn't this give 5/12 since there are 5 marbles that are not blue and not orange? $\endgroup$
    – Zeeshan Ahmad
    Sep 18, 2017 at 16:18
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    $\begingroup$ Yes, I am pretty confident that is the answer. Since one could ask well what is the probability of not orange then that would be all the blue and green balls divided by total number of balls. $\endgroup$
    – Wolfy
    Sep 18, 2017 at 19:01

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