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Math Help - 3 Quick Probability questions

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    63

    3 Quick Probability questions

    1) the secretary of a college has calculated that from the students who took calculus, physics and chemistry last semester:
    78% passed calculus
    80% passed physics
    84% chemistry
    60% calculus and physics
    65% physics and chemistry
    70% calculus and chemistry,
    and 55% all three.

    Show that these numbers are not consistent, and therefore the secretary has made a mistake

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    2) If X is uniformly distributed on {a,b}, find the moment generating function of X
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    3) that detects missing pulses. The number of errors found in an eight bit byte is a random variable with the following distribution:

    F(x)= 0 if x <1
    0.7 if 1<= x <4
    0.9 if 4<= x <7
    1 if x =>7

    find the following:


    a. P(X<=4)
    b) P(X>7)
    c) P(X<=2)
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Thanks
    539
    Hello, Andreamet!

    1) The secretary of a college has calculated that from the students
    who took calculus, physics and chemistry last semester:

    78% passed calculus
    80% passed physics
    84% passed chemistry
    60% passed calculus and physics
    65% passed physics and chemistry
    70% passed calculus and chemistry, and
    55% passed all three.

    Show that these numbers are not consistent,
    and therefore the secretary has made a mistake
    We have this formula:
    . . n(A\,\cup\,B\,\cup\,C) \;=\;n(A) + n(B) + n(C) - n(A\,\cap\,B) - n(B\,\cap\,C) - n(A\,\cap\,C) + n(A\,\cap\,B\,\cap\,C)

    Then we have:
    . . n(\text{Calc }\cup\text{ Phys } \cup\text{ Chem}) \;=\;78\%\,+\,80\%\,+\,84\%\,-\,60\%\,-\,65\%\,-\,70\%\,+\,55\% \;=\;102\%


    The data adds up to more than 100% . . . clearly impossible.

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