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A certain board game has a row of squares numbered 1 to 100. [#permalink]

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29 Feb 2012, 11:58

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Difficulty:

55% (hard)

Question Stats:

49% (01:54) correct
51% (01:24) wrong based on 61 sessions

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A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability the piece ends no more than 7 spaces from the square numbered 49?

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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29 Feb 2012, 12:12

Expert's post

metallicafan wrote:

A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability the piece ends no more than 7 spaces from the square numbered 49?

No more than 7 spaces from 49 means in the range from 49-7=42 to 49+7=56, inclusive. Total numbers in this range 56-42+1=15, the probability favorable/total=15/100=0.15.

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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29 Feb 2012, 12:18

Expert's post

AbeinOhio wrote:

Quote:

If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction

Bunuel - thanks for the response - is the quote above just to distract you from the solution or was it needed?

I read this and thought it was much more complex than 600-700 level...

Yes, "a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction" just means that a game piece is placed on a random square. _________________

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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01 Mar 2012, 07:04

Bunuel, I have a doubt: The piece must end in the range 42-56, right? Also, the question says that the game piece is placed on a random square and then moved 7 consecutive spaces in a random direction.

So, if we wanted that the piece be placed in square #42, for instance, there are two possible squares in which the piece could be originally placed: 35 and 49. If it is placed in #35 we have to move the piece to the right, and if it is placed in #49, we have to move the piece to the left. So, there are two possibilities to obtain the desired result. This happens with every square in the range 42-56.

However, if we wanted that the piece be placed in square #1, there are not two possibilities. The only square in which the piece can be originally placed is #8 (then we move it 7 squares to the left).

Based on this reasoning, the probability could not be \(\frac{15}{100}\) because there are numbers that have more succesful outcomes than others as I have shown.

I think that I am overanalyzing the problem, but I cannot solve that doubt. Thanks! _________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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01 Mar 2012, 07:08

Expert's post

metallicafan wrote:

Bunuel, I have a doubt: The piece must end in the range 42-56, right? Also, the question says that the game piece is placed on a random square and then moved 7 consecutive spaces in a random direction.

So, if we wanted that the piece be placed in square #42, for instance, there are two possible squares in which the piece could be originally placed: 35 and 49. If it is placed in #35 we have to move the piece to the right, and if it is placed in #49, we have to move the piece to the left. So, there are two possibilities to obtain the desired result. This happens with every square in the range 42-56.

However, if we wanted that the piece be placed in square #1, there are not two possibilities. The only square in which the piece can be originally placed is #8 (then we move it 7 squares to the left).

Based on this reasoning, the probability could not be \(\frac{15}{100}\) because there are numbers that have more succesful outcomes than others as I have shown.

I think that I am overanalyzing the problem, but I cannot solve that doubt. Thanks!

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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07 Jan 2013, 11:18

There are three sections of interest in this problem 1) locations (42-48) and user has to move the piece to it's right -> probability P1 -> (7/100) * (1/2) 2) location 49 is selected (User can move it any direction and is still in the limit) -> probability P2 -> 1/100 3) locations (50-56) and user has to move the piece to it's left -> probability P3 -> (7/100) *(1/2)

So total probability is (P1+P2+P3) -> 8/100 i.e 8%

First of all you should include 35 and 63. So, the range is 30 (from 28 to 62, inclusive). Next, sine the game piece is moved in a random direction, then in half of the case it will move in the wrong direction (away from the range 42-56, inclusive), thus the probability is 15/100.

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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23 May 2013, 10:25

Ok ... May be I am not getting it yet and Confusing extra numbers 35, 30, 28, 62 above ..

However if I concentrate on last part of sentence and if I understand it correct, it means that there are two ways I can fall at a number (left or right). But from either way there are equal chances of falling into the range and also equal chances of going out of the range (i.e. 42-56). Since these chances cancel each other out, it is not required to consider the direction to reach a number.. Just the range of number maters .. Am I right?

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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23 May 2013, 10:29

Expert's post

Asishp wrote:

Ok ... May be I am not getting it yet and Confusing extra numbers 35, 30, 28, 62 above ..

However if I concentrate on last part of sentence and if I understand it correct, it means that there are two ways I can fall at a number (left or right). But from either way there are equal chances of falling into the range and also equal chances of going out of the range (i.e. 42-56). Since these chances cancel each other out, it is not required to consider the direction to reach a number.. Just the range of number maters .. Am I right?

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