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Probability of exactly 1

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data
    26 out of 50 total students are tall. If 2 different students are called on at random, what is the probability that exactly one is tall?

    2. Relevant equations
    please see below


    3. The attempt at a solution
    so here's what I ended up with:
    1st student is tall: 26/50 x 24/49=312/1225
    2nd student is tall: 24/50 x 26/49= 312/1225

    I'm not sure whether I now multiply the two fractions or add them... Am I on the right track?

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 4, 2013 #2

    Dick

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    Yes, if you want to do it that way you are on exactly the right track. The two events you have are mutually exclusive. What do you think about the question of whether to add or multiply?
     
  4. Feb 5, 2013 #3
    I'm leaning towards adding, but the end result seems a little high... Would 624/1225 be the asnwer?
     
  5. Feb 5, 2013 #4

    HallsofIvy

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    Why is that "high"? It is just about 1/2 and just about 1/2 of the students are "tall".

    If A and B are "equally likely" (probability of each 1/2) then "AA", "AB", "BA", and "BB" all have probability 1/4 so AB+ BA has probability 1/2.
     
  6. Feb 5, 2013 #5

    Dick

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    Yes, it is. You can check it using the combinations formula C(n,k) if you know that. There are C(26,1) ways to choose the tall, C(24,1) ways to choose the other and C(50,2) ways total ways to choose 2 students. C(26,1)*C(24,1)/C(50,2)=624/1225.
     
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