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Standing on the origin of an xy-coordinate plane, John takes [#permalink]
13 Feb 2012, 21:36
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This post was BOOKMARKED
00:00
A
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Difficulty:
85% (hard)
Question Stats:
49% (03:19) correct
51% (02:22) wrong based on 90 sessions
Standing on the origin of an xy-coordinate plane, John takes a 1-unit step at random in one of the following 4 directions: up, down, left, or right. If he takes 3 more steps under the same random conditions, what is the probability that he winds up at the origin again?
Re: Probability PS [#permalink]
13 Feb 2012, 22:18
7
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This is the Manhattan Gmat Problem of the week this week. Extremely difficult to explain this without drawing. But lets suppose he takes a step in any one direction. Since he can take 4 different directions from there on in and he does this 3 times the total number of possibilities is \(4*4*4=64\)
Now if you start drawing on a piece of paper, you will realise that there are \(9\) such possibilities where he can end up back on the origin so answer should be \(\frac{9}{64}\). I am going to attach an image of all these possibilities along-with this post as well.
Attachment:
routes.jpg [ 90.8 KiB | Viewed 2066 times ]
Hence B _________________
"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde
Re: Probability PS [#permalink]
14 Feb 2012, 00:25
9
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Expert's post
Smita04 wrote:
Standing on the origin of an xy-coordinate plane, John takes a 1-unit step at random in one of the following 4 directions: up, down, left, or right. If he takes 3 more steps under the same random conditions, what is the probability that he winds up at the origin again?
(A) 7/64 (B) 9/64 (C) 11/64 (D) 13/64 (E) 15/64
Find the total number of possibilities first. He takes total 4 steps . He can take each step in any direction so there are a total of 4*4*4*4 possibilities (this includes UUUU, UDLR, DDLR etc etc)
He needs to be at the origin after 4 steps. So if he takes a step up, he needs to take a step down at some time. If he takes a step to the left, he needs to take one to the right at some time. Say if he takes two steps in this way - UL, his next two steps are defined - DR/RD. If instead, he takes two steps in this way - UU, his next two steps have to be DD. There are two possibilities: 1. He goes only Up and Down or only Left and Right. UUDD can be arranged in 4!/(2!*2!) ways (includes UDUD, DUDU, DDUU etc). LLRR can also be arranged in 4!/(2!*2!) ways. 2. He goes Up/Down as well as Left/Right. UDLR can be arranged in 4! ways.
Total possible arrangements = 2*4!/(2!*2!) + 4!
Probability he comes back to the origin = (2*4!/(2!*2!) + 4!)/4*4*4*4 = 9/64 _________________
Re: Standing on the origin of an xy-coordinate plane, John takes [#permalink]
26 Sep 2013, 22:31
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: Standing on the origin of an xy-coordinate plane, John takes [#permalink]
20 May 2014, 23:57
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It took me about 3.5 mins to solve...I forgot some cases initially
Total no of cases=4^4 Way 1- 1 each of L,R,U,D- They can be arranged in 4! ways..4! Way 2- 2 each of R & L..RRLL- They can be arranged in 4!/2!*2!= 6 Way 2- 2 each of D & U..DDUU- They can be arranged in 4!/2!*2!= 6
36 ways possible/4*4*4*4 =9/64
I think it helps to think directions as numbers with opposite signs...In this case the sum of the 4 numbers should be 0 _________________
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Re: Standing on the origin of an xy-coordinate plane, John takes [#permalink]
25 Jan 2016, 22:23
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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
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