document.write( "Question 1206755: It has been estimated that only about 25% 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.
\n" ); document.write( "Give the distribution of X.
\n" ); document.write( "What is the probability that we must survey just 1 or 2 residents until we find a California resident who does not have adequate earthquake supplies? (Round your answer to four decimal places.)
\n" ); document.write( "What is the probability that we must survey at least 2 California residents until we find a California resident who does not have adequate earthquake supplies? (Round your answer to four decimal places.)
\n" ); document.write( "How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies? (Round your answer to the nearest whole number.)
\n" ); document.write( "How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies? (Round your answer to the nearest whole number.) \n" ); document.write( "

Algebra.Com's Answer #844377 by ikleyn(52878) $\"\"$ $\"About$

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\n" ); document.write( "It has been estimated that only about 25% of California residents have adequate earthquake supplies.
\n" ); document.write( "Suppose we are interested in the number of California residents we must survey until we find a resident
\n" ); document.write( "who does not have adequate earthquake supplies.
\n" ); document.write( "Give the distribution of X.
\n" ); document.write( "(a) What is the probability that we must survey just 1 or 2 residents until we find a California resident
\n" ); document.write( "who does not have adequate earthquake supplies? (Round your answer to four decimal places.)
\n" ); document.write( "(b) What is the probability that we must survey at least 2 California residents until we find a California
\n" ); document.write( "resident who does not have adequate earthquake supplies? (Round your answer to four decimal places.)
\n" ); document.write( "(c) How many California residents do you expect to need to survey until you find a California resident
\n" ); document.write( "who does not have adequate earthquake supplies? (Round your answer to the nearest whole number.)
\n" ); document.write( "(d) How many California residents do you expect to need to survey until you find a California resident
\n" ); document.write( "who does have adequate earthquake supplies? (Round your answer to the nearest whole number.)
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document.write( "This distribution is a Binomial distribution with the probability of an individual success at every\r\n" );
document.write( "single trial of 25% = 0.25 (does have adequate earthquake supplies).\r\n" );
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document.write( "(a)  P(survey just 1 until we find a California resident who does not have adequate earthquake supplies) \r\n" );
document.write( "     means that first does have adequate earthquake supplies, while the second does not = \r\n" );
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document.write( "                = 0.25*(1-0.25) = 0.1875.\r\n" );
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document.write( "     P(survey just 2 until we find a California resident who does not have adequate earthquake supplies) \r\n" );
document.write( "     means that the 1st and the 2nd do have adequate earthquake supplies, while the 3rd does not = \r\n" );
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document.write( "                = 0.25*0.25*(1-0.25) = 0.046875.\r\n" );
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document.write( "(b)  Must survey at least 2 California residents until we find a California resident who does not have . . . \r\n" );
document.write( "     means that must survey either 3 with results \"yes,yes,no\",         or\r\n" );
document.write( "                            either 4 with results \"yes,yes,yes,no\",     or\r\n" );
document.write( "                            either 5 with results \"yes,yes,yes,yes,no\", or\r\n" );
document.write( "                            . . . and so on . . . \r\n" );
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document.write( "     Accordingly, the probability is \r\n" );
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document.write( "           P =  + . . . =  =  =  =  = 0.0625.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus (a) and (b) are solved, answered and explained.\r
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\n" ); document.write( "\n" ); document.write( "I left (c) and (d) unanswered, since you packed TOO many questions in one post.\r
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