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

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Senior Manager
Joined: 12 Aug 2015
Posts: 283
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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02 Nov 2015, 10:15
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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Re: A telephone number contains 10 digit, including a 3-digit  [#permalink]

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20 Jan 2019, 00:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A telephone number contains 10 digit, including a 3-digit   [#permalink] 20 Jan 2019, 00:47

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