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True/false exam, they got 5/16 but i got 1/4, probability

  1. Nov 10, 2006 #1
    Ello ello!

    I'm not sure how they are getting 5/16 as the answer.

    The question is:
    Suppose you take a true/false quiz consisting of four questions, each worth 25%. If a score of 50% or less fails the quiz, what is the probabillity that you can pass the quiz by randomly guessing each answer?

    Well here is how I broke it down...
    If you get a 50% or less you fail, so you need at least 3 out of the 4 right to get a 75%.

    I then thought, how many possible outcomes are there? Well its like tossing a coin, its either Head or Tails or in this case True or False so you have:
    2^4 = 16 possible outcomes.

    Now I thought to use combinations, you want 4 choose 3,

    Step 1: Choose first question (T or F)
    Step 2: Choose 2nd question (T or F)
    Step 3: choose 3rd qustion (T or F)
    Step 4: choose 4th question (T or F)

    but I soon realized I dont' think i can apply the multiplication rule on this, there are too many cases so i tried combinations and i said:

    4 choose 3 = 4. So the probabily i said was:
    4/16 = 1/4.

    But the answer is 5/16.

    ANy ideas?
     
  2. jcsd
  3. Nov 11, 2006 #2
    Looks fine, but you forgot the case where you get all 4 answers right. There is only one case when this happens (4 choose 4 if you want to think of it that way) thus you will get one more and so the probability will be 5/16.
     
  4. Nov 11, 2006 #3
    wewt, I forgot all about that, thanks again! I'll send you money via pay pal :P
     
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