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

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A Four digit safe code does not contain the digits 1 and 4 [#permalink]

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16 Apr 2006, 18:59
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
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16 Apr 2006, 19:29
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
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16 Apr 2006, 21:06
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
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"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, 21:16, edited 1 time in total.
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16 Apr 2006, 21:08
how about 2 and 3? You said 1 and 4.. Did you mean 1 through 4 not included?

Thanks..
VP
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16 Apr 2006, 21:15
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

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16 Apr 2006, 21:18
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
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17 Apr 2006, 11:08
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
17 Apr 2006, 11:08
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A Four digit safe code does not contain the digits 1 and 4

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