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Sarah cannot completely remember her four-digit ATM pin number

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Joined: 29 Jan 2015
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Sarah cannot completely remember her four-digit ATM pin number [#permalink]

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New post 19 May 2017, 01:38
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

78% (00:59) correct 22% (01:30) wrong based on 37 sessions

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Sarah cannot completely remember her four-digit ATM pin number. She does remember the first two digits, and she knows that each of the last two digits is greater than 5. The ATM will allow her three tries before it blocks further access. If she randomly guesses the last two digits, what is the probability that she will get access to her account?

(A) 1/2
(B) 1/4
(C) 3/16
(D) 3/18
(E) 1/32
[Reveal] Spoiler: OA

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Re: Sarah cannot completely remember her four-digit ATM pin number [#permalink]

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New post 19 May 2017, 01:54
rohan2345 wrote:
Sarah cannot completely remember her four-digit ATM pin number. She does remember the first two digits, and she knows that each of the last two digits is greater than 5. The ATM will allow her three tries before it blocks further access. If she randomly guesses the last two digits, what is the probability that she will get access to her account?

(A) 1/2
(B) 1/4
(C) 3/16
(D) 3/18
(E) 1/32


Shouldn't it be 721/4096
using 1- (15/16)^3
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Joined: 21 Aug 2013
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Re: Sarah cannot completely remember her four-digit ATM pin number [#permalink]

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New post 19 May 2017, 01:59
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First two digits are already known. For each of the last two digits, we have 4 options: 6, 7, 8 or 9.
So the last two digits can take a total of 4 * 4 = 16 values.

For a total of 16 possibilities, Sarah has three tries. So three things could happen:

1. She guesses on the first try, for which the probability is 1/16

2. She doesn't guess on first but second try. So in first try she entered a wrong code and in second try she entered a correct code.
probability of the same = 15/16 * 1/15 = 1/16.

3. First two tries wrong code, third try correct code. Probability = 15/16 * 14/15 * 1/14 = 1/16.

So total probability = 1/16 + 1/16 + 1/16 = 3/16.

Hence answer is C.
Re: Sarah cannot completely remember her four-digit ATM pin number   [#permalink] 19 May 2017, 01:59
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Sarah cannot completely remember her four-digit ATM pin number

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