document.write( "Question 1183023: a river generates a spring flood about 40% of the time. Based on these records, what is the chance that it will flood for at least three years in a row sometime during the next five years?\r
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Algebra.Com's Answer #813168 by ikleyn(52852) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The way to present the events happening in each 5-year interval is to write the 5-letter string\r\n" );
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document.write( "like this, for example (N Y N N Y), which represents \"No flood\" in the years 1,3,4 and \"Yes flood\" in the years 2,5.\r\n" );
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document.write( "Then the events having flood in 3 years in a row of 5 years are these three events\r\n" );
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document.write( "    (Y Y Y N N),  (N Y Y Y N)  and  (N N Y Y Y)\r\n" );
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document.write( "The corresponding probabilities for each of these three events are   =  = 0.02304.\r\n" );
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document.write( "Next, the events having flood in 4 years in a row of 5 years are these two events\r\n" );
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document.write( "    (Y Y Y Y N)  and  (N Y Y Y Y).\r\n" );
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document.write( "The corresponding probabilities for each of these two events are   =  = 0.01536.\r\n" );
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document.write( "Finally, the event having flood in 5 years in a row of 5 years is this unique event\r\n" );
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document.write( "    (Y Y Y Y Y).\r\n" );
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document.write( "The corresponding probability for this unique event is   = 0.01024.\r\n" );
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document.write( "The ANSWER  is the sum of these probabilities taken with their multiplicities  \r\n" );
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document.write( "    P = 3*0.02304 + 2*0.01536 + 0.01024 = 0.11008.    A N S W E R\r\n" );
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