probability

This topic contains 7 replies, has 3 voices, and was last updated by  shruti290 5 years, 4 months ago.

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  • #498

    shruti290
    Participant

    a box contains 30 red ballls,30 white balls and 30 blue balls if 10 balls are selected at random wht is the probability tht at least one color will be missing from the selection?


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  • #507

    rohit pandey
    Participant

    take three events
    A={NO RED BALL}
    B={NO BLUE BALL}
    C={NO WHITE BALL}
    SO WE NEED TO FIND P{AUBUC}=?

    SO P(A)=30C10/90C10 P(B) AND P(C) WILL BE SAME
    NOW P(A∩B)=60C10/90C10 P(B∩c) and p(A∩C) WIL BE SAME

    NOW P(A∩B∩C)=0 {CANT HAPPEN}
    SO P(AUBUC}=3*{30C10-60C10}/90C10


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    • #508

      shruti290
      Participant

      but where is the case where 2 colors will be missing?
      what i thought was tht first there are 90c10 ways in total now
      case1-draw 10 balls from the 30 red and 30 white balls tht means 60c10
      cse 2- 10 balls drawn frm 30 white and 30 blue balls tht means 60c10
      case3-10 balls frm 30 red and 30 blue tht emans 60c10
      now in all these 3 cases will also involve the cases where only red ,blue or white balss are drawn therefore to avoid double counting we subtract 3*30c10
      threfore my answer becomes
      3(60c10-30c10)/90c10


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  • #515

    rohit pandey
    Participant

    just one correction p(a)=60c10/90c10
    and p(a∩b)=30c10/90c10

    so p(aubuc)=3*{60C10-30C10}/90C10

    sorry had misplaced the values as i was sleepy

    and p(aubuc) covers the possibility of two balls not being selected.


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  • #522

    admin
    Keymaster

    Well done Rohit


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    • #523

      shruti290
      Participant

      my final answer aslo comes out to be the same. can anyone tell me what is my mistake?


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      • #530

        admin
        Keymaster

        Shruti, you have only considered the case where exactly one colour is excluded. You haven’t accounted for the case where 2 colours are excluded


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        • #532

          shruti290
          Participant

          But sir what i have done is tht first when i said tht we draw 10 balls frm 30 white and 30 blue balls so this sample will automatically include the case where either only 10 white balls are drwan or10 blue balls are drwan .so this does not becomes the case of exactly one color missing


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