probability question

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coscha: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Feb 03, 2010 11:56 am

by coscha » Wed Feb 03, 2010 11:59 am

If the probability that it will rain on any day in September is 0.3, caluclate the probability that in a given ween in September, it will rain on exactly three consecutive days.

I got 0.027...but the answer is supposed to be 0.0324

Help plz

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Source: Beat The GMAT — Problem Solving | Wed Feb 03, 2010 11:59 am

ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member; Thanked: 26 times

by ace_gre » Wed Feb 03, 2010 12:50 pm

Hi, Here is my approach.

Lets create a table with the days of the week. Consider a week from Sun - Sat. Days that rain are represented by R and no rain be X
There are 5 ways to rain on three consecutive days in a week.

Su M T W Th F Sa
R R R X X X X
X R R R X X X
X X R R R X X
X X X R R R X
X X X X R R R

Since required probability is exactly three rain days and 4 non rain days => 5 * 0.3 *0.3 *0.3 * (0.7)^4
==>0.0324

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Wed Feb 03, 2010 12:59 pm

let us take this problem as if we are asked to place 3 R (rain days) and 4 Nr(non rain days) in 7 place

condition all R has to be togather

__1 __2 __3 __4 ___5 __6__7

now R can take any value from 1 to 5 ( in order to be consecutive)
it can be done in 5C1 ways=5
now 4Nr can be arranged in 4 left places in one way ( as order does not matters)

tot ways=5
now probabilty of a rain=.3
hence for 3 rain days P=.3*.3*.3
and for 4 Nr P=.7*.7*.7*.7

fnal P=5*(.3^)*(.7^4)=.0324

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Feb 03, 2010 1:00 pm

coscha wrote:If the probability that it will rain on any day in September is 0.3, caluclate the probability that in a given week in September, it will rain on exactly three consecutive days.

I got 0.027...but the answer is supposed to be 0.0324

Help plz

The rain can start with first day (1st day 2nd day and 3rd day rains) Second day , third day or fourth day and 5th day

In case the rain starts with first day it has to rain first day second and third day, additionally it should not rain on 4th 5th 6th and 7th days ; probability = 1/3*1/3*1/3*2/3*2/3*2/3*2/3 = 16 /3^6

similarly probability for rains starting on second day is = 16/3^6... and so on so forth till 5th day

total probability = 80/3^6

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member; Thanked: 26 times

by ace_gre » Wed Feb 03, 2010 3:20 pm

Hey ajith, 0.3 = 3/10 and not 1/3..and probability of not raining is 7/10 not 2/3 ? I guess you are tired

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Feb 03, 2010 9:13 pm

ace_gre wrote:Hey ajith, 0.3 = 3/10 and not 1/3..and probability of not raining is 7/10 not 2/3 ? I guess you are tired

Ahhh I get it... I guess i am tired too, Thanks

Always borrow money from a pessimist, he doesn't expect to be paid back.

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coscha: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Feb 03, 2010 11:56 am

by coscha » Thu Feb 04, 2010 8:50 am

Thanks alot guys

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