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Probability (Set Theory)

  1. Jan 21, 2009 #1
    Suppose that one card is to be selected from a deck of 20 cards taht cointains 10 red cards numbered from 1 to 10 and 10 blue cards numbered from 1 to 10. Let A be the event that a card with an even number is selected; let B be the event that the blue card is selected; and let C be the event that a card with a number less than 5 is selected. Describe the sample spase S and describe each of the following events both in words and as subsets of S:
    a) ABC
    b) BCc
    c) A U B U C
    d) A(B U C)
    e) AcBcCc
    Please someone help me aboth the part how to describe the events in words

    I did (a) ABC={even numbered blue cards less than 5}

    total autcomes=20
    S={ R1, R2, R3...R20}
    A(even cards)={2,4,6,8,10}
    B(blue cards)={B1,B2,B3...B10}
    C(cards less than 5)={C1,C2,C3,C4}

    ABC={even numbered blue cards less than 5}={ABC2,ABC4}
    is that look okay.

    b)B[tex]\bigcap[/tex]Cc={5,6,7,8...10}
    c)A U B U C= {1, 2...10}
    d)A(B U C)={2,4,6,8,10}
    e) AcBcCc={11, 12...20}
    I am confused how to describe b) thru e). I know how to solve the problems, but describe in words I am not sure what to do. Please help. Thank you.
     
    Last edited: Jan 21, 2009
  2. jcsd
  3. Jan 21, 2009 #2
    Are you sure that your answer for B is {5,6,..,10}?

    For example doesn't that contain a red card that has a 5 on it?
     
  4. Jan 21, 2009 #3
    I think is okay, b/c B={1,2,3...10}
    C={1,2,3,4}

    The BCcc={5,6...10}.
    It is the intersection B[tex]\cap[/tex]Cc.
    and the Cc is all numbers except C.
     
  5. Jan 21, 2009 #4
    You need a better way to define things, you are using numbers to define B and C but B refers to colors whereas C refers to numbers
     
  6. Jan 21, 2009 #5
    Is it: BCc(blue cards numbered bigger than 5)={B6, B7...B10}

    the notation confuses me a lot: is it {BC6, BC7...BC10} or only {B6, B7....B10}

    I don't get it. Please explain it better, please.
     
    Last edited: Jan 21, 2009
  7. Jan 21, 2009 #6
    I would define my events as

    A = {B2, B4, ..., B10, R2, R4,...,R10} i.e. cards that have even numbers on them - both blue and red

    B = {B1, B2, ..., B10} i.e. all blue cards

    C = {B1, ..., B4, R1, ..., R4} i.e. cards that have less than 5 on them - both blue and red.

    So for part b) we want [tex] B \cap C^{c} [/tex] i.e. all the blue cards that are greater than or equal to 5 i.e. {B5, ..., B10}

    Formally we could say

    [tex] C^{c} = B_5, ..., B_{10}, R_5, ..., R_{10}[/tex]

    Now intersect that with B and you are left with [tex] B_5, ..., B_{10} [/tex]
     
  8. Jan 21, 2009 #7
    Thank you so much for your help. I get it now. I did not realize that I was doing wrong the entire problem, not just the words description.
     
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