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Thread: BB probability questions

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    An Urch Guru Pundit Swami Sage Illusionz's Avatar
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    BB probability questions

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    I'm struggling with probability problems ...can anyone recommend a good book/site for probability? It'd be deeply appreciated

    Comparison Problem


    The probability that events E and F will both occur is
    0.42

    a. The probability that event E will occur.............................b.0.58

    -----------------------

    30. In a group of 80 students, 24 are enrolled in
    geometry, 40 in biology, and 20 in both. If a
    student were randomly selected from the 80
    students, what is the probability that the student
    selected would not be enrolled in either course?

    (A) 0.20
    (B) 0.25
    (C) 0.45
    (D) 0.55
    (E) 0.60
    Expecting the world to treat you fairly because you are good is like expecting the bull not to charge because you are a vegetarian.

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    2. ans C
    using set theory
    1-P(a union B)
    1 - [p(A) + P(B) - P(A int B)]
    80/80 - [24 + 40 - 20] / 80
    (80 - 44) / 80
    36 / 80
    9/20
    4.5/10
    0.45

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    2. the answer i am getting is ( C ). 0.45 .
    prob( choosing a student doing neither course ) = 36 / 80 .
    i m uploading an image file , a venn diagram .

    1. at most one can say is that p( E) + p( F) = 1.42 .
    bcoz , p( E or F ) = p( E) + p( F) - p( E and F ) = 1 .
    => prob( E ) >= 0.42 . also prob( F ) >= 0.42 .
    so , in my view , a and b cannot be compared ( lack of info ) .

    note even if we don't assume that E & F are exhaustive like above , what p( E and F ) = 0.42 at best gives us is that prob that E occurs is at least 0.42 , and nothing more info .
    Attached Thumbnails Attached Thumbnails BB probability questions-untitled.bmp  

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    1. P(e int f) = 0.42

    P(e union f) = P(e) + P(f) - P(e int f)
    1 = P(e) + P(f) - 0.42
    P(e) + P(f) = 1.42

    P(e) = 1.42 - P(f)

    max pblity P(f) can have is 1 then max value of P(e) = 0.42

    so P(e) is less than 0.52
    so a < b

    someone pls check
    chelsea

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    chelesa if max what p(f) can have is 1 , then 0.42 is minimum what p(e) can have , not the max

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    Thanks a lot Chelsea,ecodude and arjmen .
    Expecting the world to treat you fairly because you are good is like expecting the bull not to charge because you are a vegetarian.

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