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Math Help - Finding Probability of Events

  1. #1
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    Finding Probability of Events

    Oh, hello there.
    Well then, If 70% of students have blank paper, 30% have both lined and blank paper, and 10% no paper, how many people have just lined paper?
    Thanks.
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  2. #2
    Senior Member I-Think's Avatar
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    Set Theory

    Let Set B=students who have blank paper, P(B)=0.7
    Set L=students who have lined paper, P(L)=x

    P({B}\cap{L})=0.3
    P(not {B}\cup{L})=0.1
    That is, the set of students without paper.

    You should draw a Venn diagram illustrate this

    P({B}\cup{L})=1-0.1=0.9
    P({B}\cup{L})=P(B)+P(L)-P({B}\cap{L})=0.9
               0.7+x-0.3=0.9
               x=0.5

    P(L)=0.5
    To determine percentage of people with lined paper
    P(L(alone))=P(L)-P({L}\cap{B})=0.5-0.3=0.2
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  3. #3
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    Why thank you kind sir or madam.
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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Shermert View Post
    Oh, hello there.
    Well then, If 70% of students have blank paper, 30% have both lined and blank paper, and 10% no paper, how many people have just lined paper?
    Thanks.
    you have

    B denoted to Blank just
    L denoted to lined just
    N denoted to no paper


    P(B\cup L) = .9 since there is just 10% have not paper

    P(B\cap L) = .3 since there is 30% have blank and lined

    P(B) = .7 since there is 70% have just the blank

    use

    P(A\cup B) = P(A) + P(B) - P(A\cap B )

    I think it is now easy
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  5. #5
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by I-Think View Post
    Let Set B=students who have blank paper, P(B)=0.7
    Set L=students who have lined paper, P(L)=x

    P({B}\cap{L})=0.3
    P(not {B}\cup{L})=0.1
    That is, the set of students without paper.

    You should draw a Venn diagram illustrate this

    P({B}\cup{L})=1-0.1=0.9
    P({B}\cup{L})=P(B)+P(L)-P({B}\cap{L})=0.9
               0.7+x-0.3=0.9
               x=0.5

    P(L)=0.5
    To determine percentage of people with just lined paper
    P(L(alone))=P(L)-P({L}\cap{B})=0.5-0.3=0.2
    I like to explain more see the red world
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