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Properties of Matter

  1. Dec 31, 2008 #1
    Q. There are approx 10^23 H2O molecules in a thimble of water adn 10^46 H2O molecules in the ocean. You threw a thimble of water into the ocean and it mixed uniformly. Show that if you dip a thimble of water from anywhere in the ocean that you will probably scoop up at least one of the molecules from thr original thimble.

    S. I have no idea how to even attempt answering this Q so any help appreciated.
  2. jcsd
  3. Dec 31, 2008 #2


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    When the molecules from the initial thimble have been mixed uniformly, what is the probability of picking one of those molecules out of the ocean?
  4. Dec 31, 2008 #3
    Jgens - thanks for your quick response!

    Well 10^46 is 10^23 squared. So would that mean that the ratio is 1:2 so there would be a 50% chance of picking up one of the original molecules ??
  5. Dec 31, 2008 #4


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    Not quite, n/n^2 is not necessarily equal to 1/2 (in fact it usually isn't). Try another approach for finding the probability.

    Hint: It's similar to a problem like if there are n red objects in a bag containing m items, what is the probability of picking a red object from the bag?

    Note: I think you might want to brush up on your ratios. If a ratio was 1:2 there would be a 1/3 chance of picking one of the objects.
  6. Dec 31, 2008 #5
    Oh dear probabilities aren't something I am good at. :eek:( Still very confused and not understanding this. This is a Q from a intro physics course that is supposed to be helping me to understand physics - I am more confused then ever! :eek:(
  7. Dec 31, 2008 #6


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    I'm sorry. Here's a concrete example: Suppose I have a bag with 10 objects in it. If there are 4 squares in the bag, what is the probability that I will draw out a square?

    Use similar logic to solve your initial problem.
  8. Dec 31, 2008 #7
    So the probability for your example would be 4/10 --> 2/5 (or 0.4) Is this correct?

    That would make it 10^23/10^46 ......ok need to remember how to put exponents in my calculator - will go and find manual but I think its 1/2 or 0.5 am I on the right track?
  9. Dec 31, 2008 #8


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    Yes, that's correct.

    Well, you can use your calculator. Or you could just use the fact that x^n/x^m = x^(n-m).

    Edit: Just realized the second half of you post. 1/2 is definately not correct. Remember, n^2 =/ 2n in most cases.
    Last edited: Dec 31, 2008
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