David W. answered • 05/17/15
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David W.
(Note: Special THX to Matt who took a risk -- with this forum I can edit my answer, but I don't think Matt can change his comment.)
While writing my solution in MS Word, I added the enumerated list later, as an afterthought for those who are more visually oriented. I was thinking of the case where the first marble would NOT be replaced into the bag (there are problems like that on WyzAnswers). PLZ note -- everyone makes errors (that's why we should check our work and have IV&V).
This illustrates an important principle -- don't simply listen to a presentation, think about it. Consider what you would do differently. Make sure the math results are correct and the process if good. Ask, is there a simpler/better/cheaper way? I once listened to a NASA Administrator talk about their emphasis on "faster, better, cheaper."
So (since the enumerated list is incomplete and the count of bold items don't add up to the 16 that was mentioned in the fist part of my answer), the 8 duplicate draws should be added to my list !
You may quote me, "With good people, a better process generally produces a better product."
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05/18/15
Matt H.
Thanks David, well said. The part of yours that really nailed this one conceptually was the idea that "if the first one isn't blue, the ones that come after don't matter." I think that illustrates really well what the 50% x 50% would "look" like, and I'm going to remember that phrasing when I am working with my students on problems like this one!
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05/18/15
Olivia O.
Thanks Matt and David ;3
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05/18/15
Olivia O.
But can someone give me a quick and easy answer of this question/ I still don't understand... :P
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05/18/15
David W.
As we say professionally, TMI.
The chances of drawing one of the 4 blue marbles out of a bag of 8 total marbles is 4/8 (or 50% or 0.50).
Peter puts the marble back (making 8 once more).
Now, the chances of him drawing one of the 4 blue marbles out of a bag of 8 total marbles is again 50% (if we don't care about what he got the first time, but we do!). Since the chances of drawing two blue marbles in successive draws is 50% of 50% (or 1/2 of 1/2). "Of" usually means multiply, so the probability is 0.25.
- - - -
Now that you have a number and a simple explanation, be sure that you understand it.
Then, later, take some time to read what Matt and I wrote and see if you can understand the difference between getting two blue marbles on two draws where the marbles are replaced versus getting two blue marbles in two draws where the marbles are not replace.
Shalom
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05/18/15
Matt H.
05/18/15