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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probability question
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ace_gre
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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
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
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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
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
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The rain can start with first day (1st day 2nd day and 3rd day rains) Second day , third day or fourth day and 5th daycoscha 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
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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ajith
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Ahhh I get it... I guess i am tired too, Thanksace_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
Always borrow money from a pessimist, he doesn't expect to be paid back.
