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 Amc 10 Marathon

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AIME15
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PostSubject: Amc 10 Marathon   Sat Aug 16, 2008 6:13 pm

It won't be a marathon if we don't get more people, though. Post a new problem after you solve.

A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?
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PostSubject: Re: Amc 10 Marathon   Sat Aug 16, 2008 7:34 pm

6. You can have either 0, 1, 2, 3, 4, or 5 3-point shots.

Coin A is flipped three times and coin B is flipped four times. What is the probability that the number of heads obtained from flipping the two fair coins is the same?
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AIME15
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PostSubject: Re: Amc 10 Marathon   Wed Aug 20, 2008 1:43 pm

The probability that they both get 0 heads is 1/8*1/16, or 1/128.

The probability that they both get 1 head is 3/8*1/4, or 3/32.

THe probability that they both get 2 heads is 3/8*6/16, or 18/128

THe probability that they both get 3 heads is 1/8*1/4, or 1/32.

Add up all those fractions: (im too lazy) to get your answer.

New Problem: AIME15 wants his choo-choo train to run for at least 15 days. However, it starts to break down after the 2nd day. He knows it will take 5 days for the train to completely break down. It takes him 1 hour to earn 5 dollars, and he needs 100 dollars to fix his choo-choo train. THen he has to run to the hardware store (5mph) which is 20 miles away, and buy parts (takes 15 minutes), run back (3 mph because he's weighed down) and fix his train(2 days). Can he make it in time?


Last edited by Dojo on Fri Aug 22, 2008 9:14 pm; edited 1 time in total (Reason for editing : Posted the question)
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