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# John wrote a phone number on a note that was later lost.

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John wrote a phone number on a note that was later lost. [#permalink]  18 May 2008, 22:16
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John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?

a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8
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Re: Digits Of Phone Number [#permalink]  19 May 2008, 09:25
Expert's post
B

our number: XXXX111 where X is out of {2,3,5,7} (prime numbers) or of {4,6,8,9} (not prime numbers)
The probability of getting a prime number (not a prime number) for X is 1/2

So, $$P=1-\frac{1}{2^4}-C^4_1*\frac{1}{2^4}=1-\frac{5}{16}=\frac{11}{16}$$

Edited to correct some typos
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Re: Digits Of Phone Number [#permalink]  19 May 2008, 17:02
Walker, could you explain this formula better?

tks
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Re: Digits Of Phone Number [#permalink]  19 May 2008, 19:15
Expert's post
ldpedroso wrote:
Walker, could you explain this formula better?

tks

$$P_1=\frac{1}{2^4}$$ - probability of getting 4 not prime digits

$$P_2=C^4_1*\frac{1}{2^4}$$ - probability of getting 3 not prime digits and 1 prime digit.

$$P=1-P_1-P_2$$ - probability of getting at least 2 prime digits
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Re: Digits Of Phone Number [#permalink]  20 May 2008, 14:32
Walker,

Could you explain better the formula P2? I'm not familiaa with it.

thanks again
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Re: Digits Of Phone Number [#permalink]  21 May 2008, 00:28
What is the OA.
Given explanation assumes that 1 does not occur in the first 4 places. However the question only says that 1 occurs in the last 3 places. It does not say anything about 1 not occuring anywhere else.
Re: Digits Of Phone Number   [#permalink] 21 May 2008, 00:28
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