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A telephone number contains 10 digit, including a 3-digit

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Joined: 12 Aug 2015
Posts: 290
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
A telephone number contains 10 digit, including a 3-digit  [#permalink]

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New post 02 Nov 2015, 11:15
1
so Bob is given 2 opportunities to decipher the remaining 2 digits of the code, for this task he has 5 digits to choose from.

IMPORTANT notes to bear in mind before calculation:
- picking a number for place 9 is independent from picking the number for place 10 - i.e. digits can repeat
- if Bob wastes his 1st opportunity he will have better chances to pick the right combination during his second attempt - because by that time he has already proved that one combination is invalid.

So we have all the info needed to do simple calculation:

(1) \(\frac{1}{5}\)*\(\frac{1}{5}\) = \(\frac{1}{25}\) - this is the independent event that he would win on first attempt

OR

(2.1) \(\frac{4}{5}\)*\(\frac{4}{5} = [m]\frac{16}{25}\) - he fails to choose correctly on first attempt because he picks either of the 4 wrong digits for the both places

(2.2) \(\frac{1}{4}\)*\(\frac{1}{4}\)=\(\frac{1}{16}\) - he finally chooses the correct digit out of the remaining 4 for each place independently!

AND

(2.3) Multiply the above two iterations to complete the chances for the second scenario: \(\frac{16}{25}\)*\(\frac{1}{16}\)=\(\frac{1}{25}\)

(3) Sum up \(\frac{1}{25}\)+\(\frac{1}{25}\)=\(\frac{2}{25}\)=\(\frac{50}{625}\)
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KUDO me plenty

A telephone number contains 10 digit, including a 3-digit &nbs [#permalink] 02 Nov 2015, 11:15

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