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Chances of picking a basketball team

  1. Dec 6, 2008 #1
    1. The problem statement, all variables and given/known data
    A 3 person basketball team consists of a guard, a forward and a center. If a person is chosen randomly from each of 3 different such teams, what is the probability of selecting a complete team?

    2. Relevant equations

    3. The attempt at a solution

    Well my reasoning is that for the guard on the team, I have to pick from one of the teams. So looking at one of the teams, i can pick out of 3 to be the guard. Then i have to look at the next team of which i can only pick out of 2 to be the forward and finally the last team only offers me one choice. So its (3+2+1)/9=2/3

    but the answer in the back of the book gives 2/9. something's wrong.
  2. jcsd
  3. Dec 6, 2008 #2


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    Oh badness. You have added when you should have multiplied. That should be
  4. Dec 6, 2008 #3


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    You haven't even just added. Your reasoning is completely correct. 3 choices from the first team, 2 from the second and 1 from the last. That's 3*2*1 choices that give you a complete team. How many possible choices of three regardless of whether they form a team?
  5. Dec 6, 2008 #4
    well it would be, going by your reasoning, 3*3*3=9

    But I still don't understand why you multiply instead of add.
  6. Dec 6, 2008 #5


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    3*3*3=27. Come on.
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