document.write( "Question 1200232: It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. What is the probability that we must survey just one or two California residents until we find a California resident who does not have adequate earthquake supplies? (three decimal places) \n" ); document.write( "

Algebra.Com's Answer #834330 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "It has been estimated that only about 30% of California residents have adequate earthquake supplies.
\n" ); document.write( "Suppose we are interested in the number of California residents we must survey
\n" ); document.write( "until we find a resident who does not have adequate earthquake supplies.
\n" ); document.write( "What is the probability that we must survey just one or two California residents
\n" ); document.write( "until we find a California resident who does not have adequate earthquake supplies?
\n" ); document.write( "(three decimal places)
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document.write( "We have an experiment which produces success (Yes) in 30% cases;\r\n" );
document.write( "it produces failure (No) in the rest 70% cases.\r\n" );
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document.write( "They want you calculate probability of getting sequences (Yes,No)  or (Yes,Yes,No) \r\n" );
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document.write( "and then calculate the mathematical expectation\r\n" );
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document.write( "    E = 1*P(Yes,No) + 2*P(Yes,Yes,No).   <<<---===  factor 2 in the second addend represents two \"Yes\".\r\n" );
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document.write( "This mathematical expectation will give you the answer on  \" the number of California residents \r\n" );
document.write( "we must survey until we find a resident who does not have adequate earthquake supplies \"\r\n" );
document.write( "under given restrictions. \r\n" );
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document.write( "It is easy to compute the probabilities\r\n" );
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document.write( "    P(Yes,No) = 0.3*0.7 = 0.21;  P(Yes,Yes,No) = 0.3*0.3*0.7 = 0.063.\r\n" );
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document.write( "Thus the  mathematical expectation to the problem's question is\r\n" );
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document.write( "    E = 1*P(Yes,No) + 2*P(Yes,Yes,No) = 1*(0.3*0.7) + 2*(0.3*0.3*0.7) = 0.21 + 2*0.063 = 0.336.    \r\n" );
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document.write( "The    to the problem question is this value of the mathematical expectation  E= 0.336.\r\n" );
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