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Probability question

  1. Apr 11, 2013 #1
    Question
    An expert sharpshooter misses a target 10 percent of the time.

    I have a question
    "What is the probability that the fi rst miss comes after the 3rd shot?"

    Is this as simple as 0.9^3 * 0.1?
     
  2. jcsd
  3. Apr 12, 2013 #2

    Bacle2

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    Look at the sample space :

    { HHHM, HHHHM,.....}
     
    Last edited: Apr 12, 2013
  4. Apr 12, 2013 #3

    Simon Bridge

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    Yep, the key word is "after".
     
  5. Apr 12, 2013 #4

    HallsofIvy

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    The question is "does 'after'" mean "immediately after" or would five hits and then a miss be "the first miss is after the first three shots".

    If you mean the first, then, yes, (.9)^3(.01) is correct.

    If the second, then you need to expand that to larger numbers of initial hits:
    (.9)^3(.01)+ (.9)^4(.01)+ (.9)^5(.01)+...

    You might recognize that as part of a geometric sequence and so find a simple formula for sum.
     
  6. Apr 12, 2013 #5

    ssd

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    Not 0.01 but 0.1 in all cases.:)

    It is interesting to check, if we consider the 'after case' (not immediately after) then the asked event is nothing but "3 hits in first 3 shots" (whatever happens later does not matter). Therefore the answer will be (0.9)^3.
     
    Last edited: Apr 12, 2013
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