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Math Help - probability ("at least one", "at most one") help

  1. #1
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    probability ("at least one", "at most one") help

    Two professors: Prof. Strange and Prof. Boring.

    100 published papers. 45% published by Strange. 35% published by Boring. 10% of the papers involve both professors.

    Let A denote publication by Strange
    Let B denote publication by Boring

    P(A)= .45
    P(B)= .35
    P(A intersect B) = .1

    How many of the published papers were authored by:
    a.) neither Strange nor Boring?

    addition rule: P(A union B)= P(A)+P(B)-P(A intersect B), resulting in
    P(A union B) = .7, or 70 papers involved either professor, take the compliment of P(A union B),meaning:
    30 papers have nothing to do with Strange nor Boring.

    Now, where I get confused:

    b.) How many published papers were authored by at most one of these two professors?

    How would I go about answering this?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rewtuser View Post
    Two professors: Prof. Strange and Prof. Boring.

    100 published papers. 45% published by Strange. 35% published by Boring. 10% of the papers involve both professors.

    Let A denote publication by Strange
    Let B denote publication by Boring

    P(A)= .45
    P(B)= .35
    P(A intersect B) = .1

    How many of the published papers were authored by:
    a.) neither Strange nor Boring?

    addition rule: P(A union B)= P(A)+P(B)-P(A intersect B), resulting in
    P(A union B) = .7, or 70 papers involved either professor, take the compliment of P(A union B),meaning:
    30 papers have nothing to do with Strange nor Boring.

    Now, where I get confused:

    b.) How many published papers were authored by at most one of these two professors?

    How would I go about answering this?
    P(A)+P(B) counts the papers with A as author only and the papers qith B as author only and 2 times the number of papers with both, so

    P((A union B)\(A intersection B))=P(A)+P(b)-2P(A intersection B)=0.6

    RonL
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