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

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Intern
Joined: 26 Mar 2006
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A Four digit safe code does not contain the digits 1 and 4 [#permalink]  16 Apr 2006, 17:59
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) Â¼
b) Â½
c) Â¾
d) 15/16
e) 1/16
Director
Joined: 04 Jan 2006
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Kudos [?]: 16 [0], given: 0

i am getting 13/14.

1 -P(all odd).

Available numbers: {0,2,3,5,6,7,8,9}
1-{4/7*4/8*4/8*4/8}

4/7, because the first digit cant be 0, so 4 out 7 numbers, and the rest are 4/8..

But I am not getting the required..
VP
Joined: 21 Sep 2003
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P(atleast 1 even) = 1 - P(all odd)

Choice of digits available = {0,2,3,5,6,7,8,9} --> Total 8
Odd digits = {3,5,7,9}
P(all odd) = 4/8*4/8*4/8*4/8 = 1/16

Reqd Prob = 1 - 1/16 = 15/16
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Last edited by giddi77 on 16 Apr 2006, 20:16, edited 1 time in total.
Director
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Kudos [?]: 16 [0], given: 0

how about 2 and 3? You said 1 and 4.. Did you mean 1 through 4 not included?

Thanks..
VP
Joined: 21 Sep 2003
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Kudos [?]: 39 [0], given: 0

willget800 wrote:
how about 2 and 3? You said 1 and 4.. Did you mean 1 through 4 not included?

Thanks..

Oops! My mistake. I read the Q as doesn't contain digits 1 to 4.

But My answer is correct though I will edit my post!
Availabe digits = {0,2,3,5,6,7,8,9} --> 8
Odd = {3,5,7,9} --> 4
P(odd) = 4/8*4/8*4/8*4/8 = 1/16
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Senior Manager
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willget800 wrote:
how about 2 and 3? You said 1 and 4.. Did you mean 1 through 4 not included?

Thanks..

Yeah, I think 2 and 3 should also be included. The answer remains the same though.

total of 8 numbers to choose from. (0-9 except 1&4)

4 even and 4 odd.

p = 1 - 4^4 / 8^4

= 15/16

D.

- Vipin
Senior Manager
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Kudos [?]: 3 [0], given: 0

p(NOT HAVING SINGLE EVEN DIGIT) = 4/8*4/8*4/8*4/8 = 1/16

p(HAVING ATLEAST ONE SINGLE EVEN DIGIT) = 1-1/16 = 15/16
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