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In a friendly game of Beer pong there is 1 cup that has been previously used by a person with mono. Assuming the cup is infected what are the chances that you drink the infected cup if you drink 4 cups out of the 10 in the cups triangle?

In beer pong, your partner drinks 1 cup followed by you drinking one and so on. In this game you both drink till one cup is left. That last cup is thrown out.

John
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  • What do you have so far? – soakley Feb 26 '14 at 03:12
  • No symptoms yet. So I'm not sure. Isn't it 1/10 + 1/9 + 1/8 + 1/7? – John Feb 26 '14 at 03:14
  • Well, what would your chances be if the infected cup were the first one? The second one? – soakley Feb 26 '14 at 03:19
  • 1/10 + 1/9 + 1/8 + 1/7? – John Feb 26 '14 at 03:24
  • How about this - imagine 1000 triangles of 10 cups. A thousand people do what you did, drinking 4 of the 10 cups in the triangles. If there is a single mono cup in each triangle, how many of the 1000 people do you expect to have drunk the mono cup? – soakley Feb 26 '14 at 03:26
  • hmm 400 people? so 40 percent chance? – John Feb 26 '14 at 03:31
  • Good job - you got it. Your partner has a 50 percent chance (assuming he drank 5 cups), and there is a 10 percent chance that the cup that was thrown out was the mono cup. – soakley Feb 26 '14 at 03:32

1 Answers1

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You picked 4 cups, each with a 10 percent chance of being the mono cup. Your chance is 40%.

soakley
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