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Homework Help: Probability question on school classes

  1. May 19, 2010 #1
    1. The problem statement, all variables and given/known data

    In a high-school graduating class of 100 students, 54 studied math, 69 studied history, and 35 studied both math and history. If 1 of the students is selected at random, find the probability that

    (a) the student took math or history;
    (b) the student did not take either of these subjects;
    (c) the student took history but not math.
    2. Relevant equations

    P = n/N

    3. The attempt at a solution

    Ok. I am thinking that I actually need to figure out how many students took math only and history only (pretty sure this is just algebra).

    So I know that there are 54 math students; this must include those who studied both. Thus, the number of students who studied *math only* is 54 - 35 = 19.
    Similarly, those who took History only 69 - 35 = 34.

    So for (a) P(M U H) = (19 + 34) / 100 = 53/100 ... but this is wrong. Book says 22/25. So I am off to a bad start. What am I screwing up here?
  2. jcsd
  3. May 19, 2010 #2


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    Gold Member

    "or" is an inclusive word, so you also need to include the 35 who took both math and history
  4. May 19, 2010 #3
    I guess an alternative approach to this would be

    [itex]P(M\cup H) = P(M) + P(H) - P(M\cap H)[/itex]

    where M is the math set, H is the History set, etc.​

    Just curious as to why my first attempt fails?


    I see. I was wondering about that and had somehow convinced myself that it was exclusive. In general, is "or" inclusive in probability? How about math in general?
  5. May 19, 2010 #4


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    Or is inclusive in math, probability and computer science...The only instance where "or" is exclusive , that comes to mind, is in common everyday conversational usage.
  6. May 19, 2010 #5
    Hence why my waitress never says, "that comes with soup or salad or both." :smile:
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