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.
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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+11Cr (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 #13 is picked or dime #46 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
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