document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079582>Question 1079582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ?  Help with probability, please~<BR>\n" );
document.write( "An experiment consists of tossing an unfair coin (59% chance of landing on heads) a specified number of times and recording the outcomes.<BR>\n" );
document.write( "(a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.)<BR>\n" );
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document.write( ".5000<BR>\n" );
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document.write( "Incorrect: Your answer is incorrect.<BR>\n" );
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document.write( "Does this probability change if we toss the coin three times? What if we toss the coin four times?<BR>\n" );
document.write( "The probability changes if we toss the coin four times, but does not change if we toss the coin three times.<BR>\n" );
document.write( "The probability changes if we toss the coin three times, but does not change if we toss the coin four times.    <BR>\n" );
document.write( "The probability does not change for either three or four tosses.<BR>\n" );
document.write( "The probability changes for both three and four tosses.\r<BR>\n" );
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document.write( "What probability distribution model do we use to compute these probabilities?<BR>\n" );
document.write( "normal<BR>\n" );
document.write( "geometric    <BR>\n" );
document.write( "binomial<BR>\n" );
document.write( "poisson\r<BR>\n" );
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document.write( "(b) What is the probability that the first head will occur on the fourth trial? after the fourth trial? (Use 4 decimal places.)<BR>\n" );
document.write( "P(4)	 <BR>\n" );
document.write( "P(n > 4)	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693830 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=693830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ?  Help with probability, please~<BR>\n" );
document.write( "An experiment consists of tossing an unfair coin (59% chance of landing on heads) a specified number of times and recording the outcomes.<BR>\n" );
document.write( "(a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.)<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "That's asking for the probability that the coin lands tails first, \r\n" );
document.write( "and then heads second.\r\n" );
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document.write( "P(heads) = 59% = 0.59\r\n" );
document.write( "P(tails) = 100% - 59% = 41% = 0.41\r\n" );
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document.write( "P(tails first AND heads second) = P(tails first)×P(heads second) =\r\n" );
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document.write( "(0.41)×(0.59) = 0.2419 \r\n" );
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document.write( "[Learn that \"AND\" means to multiply probabilities, while \"OR\" means\r\n" );
document.write( "to add them.\r\n" );
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document.write( "</PRE><BR>\n" );
document.write( "Does this probability change if we toss the coin three times? <BR>\n" );
document.write( "What if we toss the coin four times?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "No it doesn't change because we're only interested in what happens\r\n" );
document.write( "on the first two tosses.  It doesn't matter what happens after that.\r\n" );
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document.write( "</PRE><BR>\n" );
document.write( "What probability distribution model do we use to compute <BR>\n" );
document.write( "these probabilities?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "A BIcycle has TWO wheels.\r\n" );
document.write( "When we BIsect something we cut it into TWO parts\r\n" );
document.write( "The prefix \"BI-\" means TWO.\r\n" );
document.write( "There are TWO ways the coin can fall, 1. Heads, 2. Tails.\r\n" );
document.write( "Answer: BInomial.\r\n" );
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document.write( "</PRE><BR>\n" );
document.write( "(b) What is the probability that the first head will occur <BR>\n" );
document.write( "on the fourth trial? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That's asking for the probability that the coin lands tails first, \r\n" );
document.write( "tails second, tails third, and heads fourth.\r\n" );
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document.write( "P(heads) = 59% = 0.59\r\n" );
document.write( "P(tails) = 100% - 59% = 41% = 0.41\r\n" );
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document.write( "P(tails first AND tails second AND tails third AND heads fourth) = \r\n" );
document.write( "P(tails first)×P(tails second)×P(tails third)×P(heads fourth) =\r\n" );
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document.write( "(0.41)×(0.41)×(0.41)×(0.59) = 0.04066339, round to 0.0407 \r\n" );
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document.write( "[Again, be sure to learn that \"AND\" means to multiply probabilities, while \r\n" );
document.write( "\"OR\" means to add them.]\r\n" );
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document.write( "</PRE><BR>\n" );
document.write( "(b) What is the probability that the first head will occur... <BR>\n" );
document.write( "after the fourth trial?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "That's asking for the probability that the coin lands tails first, \r\n" );
document.write( "tails second, tails third, and tails fourth.	[It doesn't matter\r\n" );
document.write( "when the first head occurs, for if the first four tosses are tails,\r\n" );
document.write( "the first head will occur sometime AFTER the fourth trial.\r\n" );
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document.write( "P(tails first AND tails second AND tails third AND tails fourth) = \r\n" );
document.write( "P(tails first)×P(tails second)×P(tails third)×P(tails fourth) =\r\n" );
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document.write( "(0.41)×(0.41)×(0.41)×(0.41) = 0.02825761, round to 0.0283. \r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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