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A Four digit safe code does not contain the digits 1 and 4

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Senior Manager
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Joined: 19 Oct 2004
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A Four digit safe code does not contain the digits 1 and 4 [#permalink] New post 08 Nov 2004, 12:18
A Four digit safe code does not contain the digits 1 and 4 at all. What is the probability that it has at least one even digit?

a)1/4
b)1/2
c)3/4
d)15/16
e)1/16
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 [#permalink] New post 08 Nov 2004, 12:26
D)
Prob of getting odd: 1/2
Prob all 4 digits are odd: (1/2)^4 = 1/16
Prob of getting at least 1 even: 1 - 1/16 = 15/16
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 [#permalink] New post 08 Nov 2004, 16:10
My first draft was :

= 1 - Prob(all odd digits)

= 1 - 4^4/7^4

Apparently it is damned wrong... Paul could you please explain where my reasoning is flawed ? Thx
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 [#permalink] New post 08 Nov 2004, 16:45
odd digits {0,2,6,8}
even digits {3,5,7,9}
Let safe code be WXYZ
Prob of getting 1 odd digit in safe number position W: 1/2
Prob of getting 2 odd digits in safe number W and X: (1/2)^2
...
Prob of getting 4 odd digits(all) in safe number position W, X, Y and Z: (1/2)^4

Prob of getting at least 1 even is equal to 1- prob(all odd)
1 - 1/16 = 15/16

I think you mixed up the sample set where total digits should be 8(as shown in my odd/even sample set) as opposed to 7.
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Paul

  [#permalink] 08 Nov 2004, 16:45
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A Four digit safe code does not contain the digits 1 and 4

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