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# What is the probability that a 3-digit positive integer pick

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Manager
Joined: 30 May 2009
Posts: 196
What is the probability that a 3-digit positive integer pick  [#permalink]

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Updated on: 14 Sep 2013, 06:00
2
5
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:56) correct 39% (01:23) wrong based on 89 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-probability-that-a-3-digit-positive-integer-88572.html

Originally posted by sdrandom1 on 28 Jun 2009, 17:56.
Last edited by Bunuel on 14 Sep 2013, 06:00, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 07 Jun 2009
Posts: 174

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28 Jun 2009, 20:37
1
I go for C
3 digit numbers: 100-999 = 900 numbers
numbers with one or more 7 would be 07,17,27,37,47,57,67,70,71,72,73,74,75,76,77,78,79,87 and 97.
100-200= 19
201-300= 19
301-400= 19
401-500= 19
501-600= 19
601-700= 20
701-800= 99
801-900= 19
900-999= 19
Total= 252

Probability of picking a number with 7 = Numbers with 7 / all the numbers = 252/900= 7/25
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Intern
Joined: 22 Mar 2008
Posts: 1
Der is a simpler way of doing this  [#permalink]

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28 Jun 2009, 21:40
7
The total number of 3 digit numbers can be found from permutations that is 9x10x10. The digits 1,2,3,4,5,6,7,8 & 9 can be used for the first digit and the other two digits can in addition have 0 also.

The question wants us to determine 3 digit numbers with atleast one 7 in any of the digits. SO let us find out the probability that 7 does not occur anywhere. The permutation would be 8x9x9. Digits 1,2,3,4,5,6,8 & 9 as the first digit and the additional 0 for the tens and units digit.

Probability that 7 occurs once or more = 1 - Probability that 7 does not occur at all
= 1 - (8x9x9)/(9x10x10)
= 1 - 18/25
= 7/25
Math Expert
Joined: 02 Sep 2009
Posts: 50572
Re: What is the probability that a 3-digit positive integer pick  [#permalink]

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14 Sep 2013, 06:01
3
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 total 900 3 digit numbers;

3 digit number with no 7 =8*9*9=648 (first digit can take 8 values from 1 to 9 excluding 7; second and third digits can take 9 values from 0 to 9 excluding 7),

P(at least one 7)=1-P(no 7)=1-648/900=252/900=7/25

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-probability-that-a-3-digit-positive-integer-88572.html
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Posts: 8759
Re: What is the probability that a 3-digit positive integer pick  [#permalink]

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03 Nov 2018, 10:34
Hello from the GMAT Club BumpBot!

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Re: What is the probability that a 3-digit positive integer pick &nbs [#permalink] 03 Nov 2018, 10:34
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