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Math Help - Picking Marbles from a bag--Probability

  1. #1
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    Picking Marbles from a bag--Probability

    Could anyone help me out?

    There are 100 marbles in a bag, 50 blue, 40 red, and 10 purple. You draw three times returning a marble to the bag each time you draw (this makes one game). What is the probability of getting 1 purple, 1blue, and 1 red? Purple, then blue, then purple? Red, then blue, then red?

    I found out that there are 27 total possibilities, so would it just be # of times that it comes up/27 or would the probability of picking each marble play into this also?
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  2. #2
    Super Member Quacky's Avatar
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    P(Blue)=0.5, P(Red)=0.4, P(Purple)=0.1

    This is unconditional probability as the events do not affect each other.

    P(blue, red, purple once) =(0.5)(0.4)(0.1)=0.02
    That is to say:

    Blue, Red, Purple = 0.02.
    Blue, Purple, Red = 0.02
    Red, Blue, Purple = 0.02
    Red, Purple, Blue = 0.02
    Purple, Blue, Red = 0.02
    Purple, Red, Blue = 0.02

    So what is the probability of you receiving a purple, blue and red in any order?
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  3. #3
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    Oh, so it would be a 12% chance of getting purple, blue and red in any order?

    What about the other 2 then?
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  4. #4
    Super Member Quacky's Avatar
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    Follow the same format.

    As I said above, P(purple) = 0.1 and P(blue) = 0.5

    P(Purple, blue, purple) = (0.1)(0.5)(0.1) = 0.005
    So just a 0.5% chance. Note that order is important here, so you do not write out the possible combinations.

    Have an attempt at the final part yourself now.
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  5. #5
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    Then the last one would have an 8/100 chance.

    Thank you so much!
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  6. #6
    Super Member Quacky's Avatar
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    Quote Originally Posted by led23 View Post
    Then the last one would have an 8/100 chance.
    Yup.
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