probability problem with money

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 A container holds 15 quarters and 9 dimes.  Two coins are drawn one at a time. 

a.       Find the probability of getting 3 dimes, if the coins are drawn without replacement. 

 

 

 

b.      Find the probability of getting 3 quarters, if the coins are drawn with replacement.

 

Jun 2nd, 2015

Thank you for the opportunity to help you with your question!

so there are 24 coins to begin with

then we have 15 quarters and 9 dimes

and we draw 2 coins at a time 

as im sure you can tell we have repetition and since it does not seem orders matter we can use combinations. so doing n+1-1Cr (n=24(total items) and r= how many are being taken) we get 2600 repetitions

now there is only 1 in which all 3 dimes can be picked since it does not matter if dime #1-3 is picked or dime #4-6 is picked it is still counted as one. so the probability is 1/2600.

now for the second one it is similar to the first in which this case they are replaced so the probability of drawing a coin does not change since we replace them after each one. which means the probaiblity is 15/24^3=.244. This is because it does not change the probability as we pick the coins up


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 2nd, 2015

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