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## Re: [ascent CAT] Questions on Probability

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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
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.

or

=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

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?

Regards
Anil

Ascent Education
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Class for CAT, XAT, GRE, GMAT
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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
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

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?

Regards
Anil

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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
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

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?

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
• 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?
>
>
> Regards
> Anil
>
>

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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)
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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• 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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>
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> 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
>
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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
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
> >
> >
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> >
> >
> >
> >
> >
> >
>
>
>
>
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