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A password of a computer used five digits where they are fro

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A password of a computer used five digits where they are fro  [#permalink]

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New post 06 May 2014, 07:23
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A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2
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Re: A password of a computer used five digits  [#permalink]

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New post 06 May 2014, 07:47
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We have five digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 =1/32 (A)
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Re: A password of a computer used five digits  [#permalink]

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New post 06 May 2014, 07:55
How can we have probability for 1st digit as 5/10, if 0 gets selected at first place its no longer a 5 digit number...
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Re: A password of a computer used five digits  [#permalink]

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New post 06 May 2014, 08:29
1
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2

How can we have probability for 1st digit as 5/10, if 0 gets selected at first place its no longer a 5 digit number...


A 5-digit number cannot have 0 as its first digit while a 5-digit password can. For example, a password can be 00000.

Does this make sense?
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 06 May 2014, 23:15
oh o..missed that. Thanks Bunuel.
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 27 Jun 2014, 16:36
For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ? :oops:
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 28 Jun 2014, 04:58
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1
maggie27 wrote:
For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ? :oops:


For two reasons.

1. 10C5 gives the number of groups of 5 possible out of 10 when the order of the selection is not important. In passwords the order of the numbers is important

2. 10C5 gives 5 different numbers out of 10, while the numbers in passwords can be repeated.

Thus the total number of passwords is 10*10*10*10*10 (10 options for each of the 5 digits we have in the password).

Hope it's clear.
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 28 Jun 2014, 07:13
Thank You so much Bunuel :)
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 29 Sep 2014, 22:43
I got stuck looking for combination approach here, it was tempting. After shifting direct probability easily found that
it is just
(1/2)^5=1/32

i thing direct method is better anyway
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 24 Feb 2016, 07:33
good question.. but it should be given that the numbers may repeat.
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 10 May 2018, 10:42
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aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


The total number of ways to select 5 digits to form a 5-digit password is 10^5. The number of ways to select the 5 digits that are either a prime (2, 3, 5, 7) or zero is 5^5. Therefore, the probability is 5^5/10^5 = (5/10)^5 = (1/2)^5 = 1/32.

Answer: A
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 22 May 2018, 05:03
How do we know whether the repetition of ghe digits are allowed or not.
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 22 May 2018, 05:38
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 18 Dec 2018, 23:21
Total possible ways of designing a password = 105ways.
No of 0’s and prime no between 0 and 9 = 5 (1,2,3,5,7)
So, The probability of favorable arrangements = 105/55 = 1/32.
Hence, a is the answer.
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Re: A password of a computer used five digits where they are fro  [#permalink]

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New post 16 May 2019, 09:04
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


total such no
0,2,3,5,7
5/10 ; 1/2
for 5 digits; (1/2)^5 = 1/32
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Re: A password of a computer used five digits where they are fro   [#permalink] 16 May 2019, 09:04
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