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# Jane needs to walk 3 blocks south and 3 blocks east. What is the proba

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Math Expert
Joined: 02 Sep 2009
Posts: 56359
Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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17 Jun 2019, 01:42
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Difficulty:

45% (medium)

Question Stats:

46% (01:17) correct 54% (01:31) wrong based on 24 sessions

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Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

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Posts: 566
Location: India
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Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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17 Jun 2019, 03:05
6
Bunuel wrote:
Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

To reach destination, Jane needs to cover 3S & 3E blocks
--> Total ways to reach = number of ways of arranging 3S & 3E = $$\frac{6!}{3!*3!}$$ = 20

Favorable = Taking first 2 south blocks = "Fixing" the first 2 as SS and arranging remaining 1S & 3E = $$\frac{4!}{1!*3!}$$ = 4

Required Probability = 1/5

IMO Option B

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Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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Updated on: 17 Jun 2019, 23:29
3
Answer should be 1/5 as she is moving south first 2 steps means that she is not moving east. So
Total options-6
East-3
South-3

P(moving south) = 3/6 * 2/5 = 1/5

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Posted from GMAT ToolKit

Originally posted by himani2093 on 17 Jun 2019, 01:56.
Last edited by himani2093 on 17 Jun 2019, 23:29, edited 1 time in total.
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Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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17 Jun 2019, 11:58
Bunuel wrote:
Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

total ways initially ; 6!/3!*3! = 20
and now keeping 2 blocks fixed and 3 blocks east as options we have 4!/3! ways ; 4
4/20 ; 1/5 IMO B
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Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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17 Jun 2019, 12:17
Bunuel wrote:
Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

It is quite confusing at first if you miss a single thing

There are 3S and 3E

How do you arrange that????

6!/(3!3!) These are total number of ways

Now we have to fix first two as S

(S S) (4 OTHERS (3E, 1S))

The way these can be arranged
4!/3!

not 5!/3! because you've fixed the first two

(4!/3!)/(6!/3!3!)

Ans: 1/5

I hope this helps
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Joined: 23 Jul 2015
Posts: 57
Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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17 Jun 2019, 17:58
Dillesh4096 wrote:
Bunuel wrote:
Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

To reach destination, Jane needs to cover 3S & 3E blocks
--> Total ways to reach = number of ways of arranging 3S & 3E = $$\frac{6!}{3!*3!}$$ = 20

Favorable = Taking first 2 south blocks = "Fixing" the first 2 as SS and arranging remaining 1S & 3E = $$\frac{4!}{1!*3!}$$ = 4

Required Probability = 1/5

Hey! What does 'keeping 2 blocks fixed' mean?

IMO Option B

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Posts: 14
Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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19 Jun 2019, 08:33
2
Bunuel wrote:
Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

favourable outcomes= 3c2
total outcomes = 6c2
p=3/15=1/5

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Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba  [#permalink]

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21 Jun 2019, 11:29
Bunuel wrote:
Jane needs to walk 3 blocks south and 3 blocks east. What is the probability that she will walk south for the first 2 blocks?

A. 1/6
B. 1/5
C. 2/5
D. 3/5
E. 4/5

Assuming Jane will not walk north or west, she will walk south three blocks and east three blocks; totalling six blocks. The probability that the first block she walks is south is 3/6 = 1/2. After walking one block south, she needs to walk two more blocks south and three blocks east. Thus, the probability that the second block she walks is also south is 2/5. In total, the probability that the first two blocks she walks are both south is 1/2 x 2/5 = 1/5.

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Re: Jane needs to walk 3 blocks south and 3 blocks east. What is the proba   [#permalink] 21 Jun 2019, 11:29
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