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Re: [ascent CAT] Questions on Probability

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  • vipul taneja
    1) The 2 is dumped bcos thr r 2 cases in which either 1 st or 2 nd student gets all three prizes, which is against the condition that exactly two dont get
    Message 1 of 10 , Jul 18, 2004
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      1) The 2 is dumped bcos thr r 2 cases in which either
      1'st or 2'nd student gets all three prizes, which is
      against the condition that exactly two dont get
      prizes.


      2) Answer = Prob(two head) + Prob(three heads) +
      Prob(four heads)

      or

      Answer = 1 - Prob(one head)- Prob(no heads)

      =1-(4/16)-(1/16)
      =11/16





      --- Anil kumar Babu <anil.babu@...> wrote:
      ---------------------------------
      Hi
      The following are questions from an institute book.

      1)Three different prizes are to be distributed among 4
      different
      students. Each student can get 0 to 3 prizes. If all
      prizes are
      distributed, find ways possible such that exactly 2
      students do not
      receive a prize.

      4C2 * 2^3 is my answer but the solution set indicates
      4C2(2^3 - 2).

      I dont understand why that 2 should be dumped.

      2) What is the probability that we get atleast 2 heads
      when 4 coins
      are thrown simultaneously?

      Explanations please.

      Regards
      Anil



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    • Pankaj Gautam
      Answer to the 2nd question is like this P(atleast 2H) = (total possible outcomes - total outcomes with no head - total outcomes with 1 Head) / total possible
      Message 2 of 10 , Jul 18, 2004
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        Answer to the 2nd question is like this

        P(atleast 2H) = (total possible outcomes - total outcomes with no head - total outcomes with 1 Head) / total possible   outcomes

        therefore P(atleast 2H) = (2^4 - 1 - 4) / 2^4

                                                      = 11/16


        regards
        Pankaj


        Anil kumar Babu <anil.babu@...>

        07/14/2004 07:59 PM

        Please respond to
        ascent4cat@yahoogroups.com

        To
        ascent4cat@yahoogroups.com
        cc
        Subject
        [ascent CAT] Questions on Probability





        Hi
        The following are questions from an institute book.

        1)Three different prizes are to be distributed among 4 different
        students. Each student can get 0 to 3 prizes. If all prizes are
        distributed, find ways possible such that exactly 2 students do not
        receive a prize.

        4C2 * 2^3 is my answer but the solution set indicates 4C2(2^3 - 2).

        I dont understand why that 2 should be dumped.

        2) What is the probability that we get atleast 2 heads when 4 coins
        are thrown simultaneously?

        Explanations please.

        Regards
        Anil



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      • Santosh Banerjee (Bangalore)
        Hi, The solutions go like these ... 1 let s first select 2 students who are not going to be given any prize..This can be done in 4C2 ways. Now we are left
        Message 3 of 10 , Jul 19, 2004
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          Hi,

          The solutions go like these ...

          1> let's first select 2 students who are not going to be given any prize..This can be done in 4C2 ways.

          Now we are left with 2 students and 3 prizes.

          The constraint is : Each of these 2 students must get at least 1 prize.

          so the possible combintaions are as follows

          Student1 Student2
          no. of prizes 1 2
          --------------------------------------------------
          no. of prizes 2 1

          So the no. of ways the distribution can be achieved under the above constraint is 3C1 * 2C2 + 3C2 * 1C1 = 6 .

          Therefore the total no. of possible ways = 4C2*6 = 4C2(2^3 - 2)


          2> Let's denote the event of getting at least 2 heads by E

          We note that p(E) = 1 - p(E') where E' is the complement of E

          i.e. E' is the event of getting at most 1 head.

          The sample space of E' is { TTTT, THHH, HTHH, HHTH, HHHT}

          p(E') = 4C4*(1/2)^4 + 4C3*(1/2)^3*(1/2)^1 ( P(T) = 1/2=P(H))

          = 5/16
          So, p(E) = 1- 5/16 = 11/16


          -----Original Message-----
          From: Anil kumar Babu [mailto:anil.babu@...]
          Sent: Wednesday, July 14, 2004 7:59 PM
          To: ascent4cat@yahoogroups.com
          Subject: [ascent CAT] Questions on Probability


          Hi
          The following are questions from an institute book.

          1)Three different prizes are to be distributed among 4 different
          students. Each student can get 0 to 3 prizes. If all prizes are
          distributed, find ways possible such that exactly 2 students do not
          receive a prize.

          4C2 * 2^3 is my answer but the solution set indicates 4C2(2^3 - 2).

          I dont understand why that 2 should be dumped.

          2) What is the probability that we get atleast 2 heads when 4 coins
          are thrown simultaneously?

          Explanations please.

          Regards
          Anil




          Ascent Education
          An IIM Alumni Venture
          Class for CAT, XAT, GRE, GMAT
          http://www.ascenteducation.com

          Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml
          Yahoo! Groups Links
        • devansh shah
          atleast 2 means it can be 2 , 3 or 4 so u can count -[hhhh],[hhht]*4,[hhtt]*2,[httt]*4, 1+4+2+4=11 total possi.=16 so ans will be 11/16 ...
          Message 4 of 10 , Jul 30, 2004
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            atleast 2 means it can be 2 , 3 or 4 so u can count
            -[hhhh],[hhht]*4,[hhtt]*2,[httt]*4,
            1+4+2+4=11
            total possi.=16
            so ans will be 11/16
            --- Anil kumar Babu <anil.babu@...> wrote:

            > Hi
            > The following are questions from an institute book.
            >
            > 1)Three different prizes are to be distributed among
            > 4 different
            > students. Each student can get 0 to 3 prizes. If all
            > prizes are
            > distributed, find ways possible such that exactly 2
            > students do not
            > receive a prize.
            >
            > 4C2 * 2^3 is my answer but the solution set
            > indicates 4C2(2^3 - 2).
            >
            > I dont understand why that 2 should be dumped.
            >
            > 2) What is the probability that we get atleast 2
            > heads when 4 coins
            > are thrown simultaneously?
            >
            > Explanations please.
            >
            > Regards
            > Anil
            >
            >




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          • sanoop unni
            solve this: 1) 10 cu.cm of ink can write ,on an average,340 words ,how many can one write with 0.568 litres of ink? (a)4828 (b)8484 (c) 19312 (d) 24467 2)
            Message 5 of 10 , Jul 31, 2004
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              solve this:
              1) 10 cu.cm of ink can write ,on an average,340 words
              ,how many can one write with 0.568 litres of ink?
              (a)4828 (b)8484 (c) 19312 (d) 24467

              2) Fresh grapes contain 84% water while raisins
              contain 20% water.how many Kg of raisins can be made
              from
              80 Kg of grapes?
              (a)16 kg (b) 18 kg (c) 20 kg (d) 22 kg

              3) A shop keeper mixes 3 varieties of rice costing Rs
              10,12,17 per Kg.In what ratio should they be mixed so
              that the
              resulting mixture can be sold at Rs 15.60 per kg
              making 20% profit?
              (a) 9:14:36 (b) 11:14:25 (c) 14:36:43 (d) 2:6:3




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            • vinu chandran
              hii... 1. ie 1 cc -- 34 words.. if i litre = 1000cc = .568litre = 568 cc.. so answer = 568 * 34 = some no. ending in 2..as there is only 1 such option..ie
              Message 6 of 10 , Aug 24, 2004
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                hii...
                1. ie 1 cc --> 34 words..
                if i litre = 1000cc => .568litre = 568 cc..
                so answer = 568 * 34 = some no. ending in 2..as there
                is only 1 such option..ie 19312... go 4 it.. :D

                2. dats 16% matter in grapes n 80% matter in raisins..
                so .16 * 80 matter multiplied by 1.25 2 get raisins..
                so answer = .16*80*1.25 = 16kg

                3.--- sanoop unni <sanoop_u@...> wrote:

                >
                > solve this:
                > 1) 10 cu.cm of ink can write ,on an average,340
                > words
                > ,how many can one write with 0.568 litres of ink?
                > (a)4828 (b)8484 (c) 19312 (d) 24467
                >
                > 2) Fresh grapes contain 84% water while raisins
                > contain 20% water.how many Kg of raisins can be made
                > from
                > 80 Kg of grapes?
                > (a)16 kg (b) 18 kg (c) 20 kg (d) 22 kg
                >
                > 3) A shop keeper mixes 3 varieties of rice costing
                > Rs
                > 10,12,17 per Kg.In what ratio should they be mixed
                > so
                > that the
                > resulting mixture can be sold at Rs 15.60 per kg
                > making 20% profit?
                > (a) 9:14:36 (b) 11:14:25 (c) 14:36:43 (d) 2:6:3
                >
                >
                >
                >
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              • atryee2000
                I am getting the answer to the 3rd question 1:1:1 sp after profit of 20% =15.60 thus sp without profit=13 thus using alligation 10 17 13 4 3 4:3 12 17
                Message 7 of 10 , Sep 9, 2004
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                  I am getting the answer to the 3rd question 1:1:1

                  sp after profit of 20% =15.60
                  thus sp without profit=13

                  thus using alligation

                  10 17
                  13
                  4 3

                  4:3

                  12 17
                  13
                  4 1
                  4:1

                  thus final ratio

                  4:4:(3+1)

                  = 1:1:1








                  --- In ascent4cat@yahoogroups.com, vinu chandran <vinu12120@y...> wrote:
                  > hii...
                  > 1. ie 1 cc --> 34 words..
                  > if i litre = 1000cc => .568litre = 568 cc..
                  > so answer = 568 * 34 = some no. ending in 2..as there
                  > is only 1 such option..ie 19312... go 4 it.. :D
                  >
                  > 2. dats 16% matter in grapes n 80% matter in raisins..
                  > so .16 * 80 matter multiplied by 1.25 2 get raisins..
                  > so answer = .16*80*1.25 = 16kg
                  >
                  > 3.--- sanoop unni <sanoop_u@y...> wrote:
                  >
                  > >
                  > > solve this:
                  > > 1) 10 cu.cm of ink can write ,on an average,340
                  > > words
                  > > ,how many can one write with 0.568 litres of ink?
                  > > (a)4828 (b)8484 (c) 19312 (d) 24467
                  > >
                  > > 2) Fresh grapes contain 84% water while raisins
                  > > contain 20% water.how many Kg of raisins can be made
                  > > from
                  > > 80 Kg of grapes?
                  > > (a)16 kg (b) 18 kg (c) 20 kg (d) 22 kg
                  > >
                  > > 3) A shop keeper mixes 3 varieties of rice costing
                  > > Rs
                  > > 10,12,17 per Kg.In what ratio should they be mixed
                  > > so
                  > > that the
                  > > resulting mixture can be sold at Rs 15.60 per kg
                  > > making 20% profit?
                  > > (a) 9:14:36 (b) 11:14:25 (c) 14:36:43 (d) 2:6:3
                  > >
                  > >
                  > >
                  > >
                  > > __________________________________
                  > > Do you Yahoo!?
                  > > New and Improved Yahoo! Mail - Send 10MB messages!
                  > > http://promotions.yahoo.com/new_mail
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                  > >
                  > >
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                  > > --------------------~-->
                  > > Yahoo! Domains - Claim yours for only $14.70
                  > >
                  > http://us.click.yahoo.com/Z1wmxD/DREIAA/yQLSAA/DxDolB/TM
                  > >
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                  > >
                  > >
                  > > Ascent Education
                  > > An IIM Alumni Venture
                  > > Class for CAT, XAT, GRE, GMAT
                  > > http://www.ascenteducation.com
                  > >
                  > > Archives of past CAT questions can be viewed at
                  > >
                  >
                  http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml
                  > >
                  > > Yahoo! Groups Links
                  > >
                  > >
                  > > ascent4cat-unsubscribe@yahoogroups.com
                  > >
                  > >
                  > >
                  > >
                  > >
                  > >
                  >
                  >
                  >
                  >
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