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

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Intern
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Joined: 17 May 2014
Posts: 36
Re: A telephone number contains 10 digit, including a 3-digit  [#permalink]

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New post 18 May 2014, 05:05
JusTLucK04 wrote:
mittalg wrote:
JusTLucK04 wrote:
I guess he is hitting randomly here and the probability that he chooses a number at any point of time is equal..
1/25+24/25*1/25= 49/625
It should be explicitly stated if he is trying numbers in an order/not repeating...I think


I think most of the answers are missing a point. Let me try to put it across:

Total number of possible numbers are : 5x5 = 25

Correct number =1

Case 1: When he gets it right in first attempt: P(E1) = 1/25

Case 2: He gets 1st attempt wrong and second right:

When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24

Thus, P(E2) = 24/25 x 1/24

=1/25

Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (E) is therefore right as most of you mentioned but the method employed was wrong.

Cheers!!!


Whats wrong with my method..Can you please elaborate?..Wasn't able to catch you here

I mean to imply that he is not taking a note of the numbers hit earlier and is just going about randomly..as nothing has been mentioned
Anyways this is trivial and GMAC will be more specific..Skip it


It makes sense that he doesn't dial the same number again. Therefore, option he would have the 2nd time are 24 instead of 25. It might be trivial in this question as you are anyways getting the right answer, but it may become important in some other place. Thought it is always good to know the right solution irrespective of the fact whether you are getting a write answer or not.

Anyways don't bother much.

Cheers!!
Intern
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Joined: 18 Mar 2019
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Re: A telephone number contains 10 digit, including a 3-digit  [#permalink]

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New post 02 Jul 2019, 10:38
srp wrote:
I am getting E (as closest)

Remaining numbers to fill last two digits (3,4,6,8,9): Total 5

Probability of choosing right numbers in two places = 1/5 * 1/5 = 1/25
Probability of not choosing right numbers in two places = 1-1/25 = 24/25
--
At most two attempts: 1) Wrong-1st Attempt, Right - 2nd, 2) Right - 1st Attempt
1) = 24/25 * 1/25 = 24/625
2) = 1/25

Add 1 and 2, 24/625 + 1/25 = 49/625 ~ 50/625


In case 1, when you attempted for the 1st time and got it wrong, 1 possibility out of 25 is exhausted. You are left with only 24 possibilities. So, the second attempts outcome should be measured on the remaining 24 possibilities only.

Then you will get the exact answer.
=(24/25)*(1/24)+(1/25)
=1/25 + 1/25
=2/25 which is same as 50/625.

Hope this helped.

Please correct me if I am wrong. Thank you.

Posted from my mobile device
GMAT Club Bot
Re: A telephone number contains 10 digit, including a 3-digit   [#permalink] 02 Jul 2019, 10:38

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