Solve Mystery: Properties of Matter Q: Thimble of Water in Ocean

[NZ-Minty]

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.

 

[jgens]

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?

 

[NZ-Minty]

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 ??

 

[jgens]

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.

 

[NZ-Minty]

Oh dear probabilities aren't something I am good at. ( 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! (

 

[jgens]

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.

 

[NZ-Minty]

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?

 

[jgens]

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 definitely not correct. Remember, n^2 =/ 2n in most cases.