probability haunts

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gmatnmein2010: Master | Next Rank: 500 Posts; Posts: 185; Joined: Thu Feb 04, 2010 3:06 am; Thanked: 6 times

by gmatnmein2010 » Mon Feb 08, 2010 5:34 am

2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

pls suggest books to improve my probability

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 5:34 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 5:39 am

gmatnmein2010 wrote:2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

pls suggest books to improve my probability

Solve a book of probability by K.C.Sinha , or a problem book of IIT-JEE by TMH, or problem plus by aschit Das gupta.

Solve any good book of IIT-JEE . you will surely be able to solve any problem.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 5:49 am

gmatnmein2010 wrote:2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

pls suggest books to improve my probability

Total no. of 3 digit = 999-99 =100
total no. of required 3- digits which can be formed = either 1 7's , 2 7's , all 3 7's
= (8.9.1+9.1.9+1.9.9)+(1.1.9+1.9.1+8.1.1)+1.1.1=72+81+81+9+9+8+1 = 271

Ans A

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Mon Feb 08, 2010 6:48 am

imo c

Total 3 digit numbers 900, 3 digit number with no 7 =8*9*9=648, P(at least one 7)=1-P(no 7)=1-648/900=252/900=7/25

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roh00kan: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Thu Oct 30, 2008 10:36 pm; Thanked: 3 times

by roh00kan » Sat Aug 28, 2010 1:40 am

What's the Official Answer?

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Sat Aug 28, 2010 6:22 am

thephoenix wrote:imo c

Total 3 digit numbers 900, 3 digit number with no 7 =8*9*9=648, P(at least one 7)=1-P(no 7)=1-648/900=252/900=7/25

i got that too, but counting each hundreds, tens and units digit.... how do u come up with 8*9*9?

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Sat Aug 28, 2010 8:47 am

gmatnmein2010 wrote:2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

There are only 10 numbers : {0,1,2,3,4,5,6,7,8,9}

You want 1 or more = 7.

So the probability of the first one being 7 is 1/10
second one being 7 = 1/10 and third one = 1/10

1/10+1/10+1/10=3/30=1/10

So (E).

Isnt this the way to do it guys?

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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ramana: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jan 27, 2009 8:40 pm; Thanked: 1 times

by ramana » Sat Aug 28, 2010 8:59 am

This is how i solved.

probability :- 1 - ( non-favorable outcomes /total no: of outcomes )

Total NO: we have three digits and 10 digits (0-9)

last digit can be anyone in the range[0 9] : 10
middle digit can be anyone in the range[0 9] : 10
first Digit cannot be '0' -> [1 9] : 9

total 9*10*10 =900

NON- Favorable outcomes : No digit should contain 7 and the first place should not have 0 and 7

thus we have 8*9*9 = 648

apply the formula for Prob stated above,

= 252/900 reduced to 7/25

IMO C

what is the OA?

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sat Aug 28, 2010 9:55 am

gmatnmein2010 wrote:2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

pls suggest books to improve my probability

i would solve it simply like this
supposed ABC is a 3-digit positive integer
there are 10 numbers from 0 to 9 and A cant be 0 thus we will have 9*10*10=900
if only A = 7, we will have 9*9=81 ways to select B and C
if only B or C = 7 we will have only 9*8+9*8=72*2=144 ways to select a and C/B
if only AB or AC=7 we will have only 2*9=18 ways to select C or B, respectively
if only BC=7 we will have only 8 ways to select A because A cant be 0 or 7 anymore
if ABC all = 7 we will have 1 way to select em
thus totally we will have 144
+81+18+8+1=252 ways
so the probability will be 252/900 or 7/25
C is the answer
hope it helps

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Sat Aug 28, 2010 10:06 am

ramana wrote:This is how i solved.

probability :- 1 - ( non-favorable outcomes /total no: of outcomes )

Total NO: we have three digits and 10 digits (0-9)

last digit can be anyone in the range[0 9] : 10
middle digit can be anyone in the range[0 9] : 10
first Digit cannot be '0' -> [1 9] : 9

total 9*10*10 =900

NON- Favorable outcomes : No digit should contain 7 and the first place should not have 0 and 7

thus we have 8*9*9 = 648

apply the formula for Prob stated above,

= 252/900 reduced to 7/25

IMO C

what is the OA?

Why can't the first place have 7???

What do you mean?

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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ramana: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jan 27, 2009 8:40 pm; Thanked: 1 times

by ramana » Sat Aug 28, 2010 10:12 am

Gurpinder wrote:
ramana wrote:This is how i solved.

probability :- 1 - ( non-favorable outcomes /total no: of outcomes )

Total NO: we have three digits and 10 digits (0-9)

last digit can be anyone in the range[0 9] : 10
middle digit can be anyone in the range[0 9] : 10
first Digit cannot be '0' -> [1 9] : 9

total 9*10*10 =900

NON- Favorable outcomes : No digit should contain 7 and the first place should not have 0 and 7

thus we have 8*9*9 = 648

apply the formula for Prob stated above,

= 252/900 reduced to 7/25

IMO C

what is the OA?
Why can't the first place have 7???

What do you mean?

favorable outcomes according to question stem - one or more 7 in a three digit number selected.

I am going for the non-favorable outcome which should be ' Number selected at random has no '7' in it'

clears?

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Sat Aug 28, 2010 10:16 am

Hey,

No, I get what you are doing. You took all the non favorable outcomes. But I am just confused with your wording "the first place should not have 0 and 7". Why can't the first number be 7? The question said 1 or more 7's. So all 3 could be 7.

Do you get what i am saying?

thanks,

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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ramana: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jan 27, 2009 8:40 pm; Thanked: 1 times

by ramana » Sat Aug 28, 2010 10:22 am

Gurpinder wrote:Hey,

No, I get what you are doing. You took all the non favorable outcomes. But I am just confused with your wording "the first place should not have 0 and 7". Why can't the first number be 7? The question said 1 or more 7's. So all 3 could be 7.

Do you get what i am saying?

thanks,

hmm, that condition is applied only for counting non-favorable outcomes.

of course the first digit can be 7 according to the question stem.

have i answered your question now?

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Sat Aug 28, 2010 10:23 am

ramana wrote:
Gurpinder wrote:Hey,

No, I get what you are doing. You took all the non favorable outcomes. But I am just confused with your wording "the first place should not have 0 and 7". Why can't the first number be 7? The question said 1 or more 7's. So all 3 could be 7.

Do you get what i am saying?

thanks,
hmm, that condition is applied only for counting non-favorable outcomes.

of course the first digit can be 7 according to the question stem.

have i answered your question now?

Yes,

Thanks

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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Maciek: Master | Next Rank: 500 Posts; Posts: 164; Joined: Sun Jul 18, 2010 5:26 amFollowed by: 4 members; Thanked: 49 times; GMAT Score:710

by Maciek » Sat Aug 28, 2010 10:32 am

Hi all!

this is wrong approach

number of possible outcomes
9 * 10 * 10 = 900
how many units are 7?
9 * 10 = 90
how many tens are 7?
9 * 9 = 81
how many hundreds are 7?
1*10*10 = 100
number of wanted outcomes
271
the probability is 271/900
it is choice A but it is wrong

hope it helps!
Best,
Maciek

Last edited by Maciek on Sat Aug 28, 2010 10:52 am, edited 1 time in total.

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