document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186837>Question 1186837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem VI  -  [14 points] A “fair,” “relatively thick” coin, when flipped, can<BR>\n" );
document.write( "show heads (H) or tails (T) with equal probabilities, but it is also probable to<BR>\n" );
document.write( "come to rest on its edge (E) with a probability of 4.5% (0.045).  Showing your<BR>\n" );
document.write( "work, answer the following questions:\r<BR>\n" );
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document.write( "1.	Set up a probability distribution table for the three possible events.\r<BR>\n" );
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document.write( "2.	If the coin were flipped twice, what would be the probability that it<BR>\n" );
document.write( "would show tails the first time and would come to rest on its edge the second<BR>\n" );
document.write( "time?  Provide a brief explanation to support your computation(s).  Show the<BR>\n" );
document.write( "probability value in 4 decimal places.\r<BR>\n" );
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document.write( "3. If the coin were flipped 14 times, what would be the probability that the<BR>\n" );
document.write( "coin would come to rest on its edge (“getting edge”) at most twice?  Showing<BR>\n" );
document.write( "your work, report the probability value in 4 decimal places.  Treat the problem<BR>\n" );
document.write( "as a binomial experiment.\r<BR>\n" );
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document.write( "4.	Determine the probability of getting heads between 4 to 6 times (both<BR>\n" );
document.write( "inclusive), i.e., 4 times, 5 times, or 6 times, when the coin is flipped 14<BR>\n" );
document.write( "times.  Showing your work, report the probability value in 4 decimal places.<BR>\n" );
document.write( "Treat the problem as a binomial experiment.\r<BR>\n" );
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document.write( "5.	What is the probability of getting “heads or tails” at least once when<BR>\n" );
document.write( "the coin is flipped 14 times? Showing your work, report the probability value in<BR>\n" );
document.write( "4 decimal places.  Treat the problem as a binomial experiment.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817857 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</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=817857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem VI - [14 points] A “fair,” “relatively thick” coin, when flipped, can <BR>\n" );
document.write( "show heads (H) or tails (T) with equal probabilities, but it is also probable to<BR>\n" );
document.write( "come to rest on its edge (E) with a probability of 4.5% (0.045). Showing your <BR>\n" );
document.write( "work, answer the following questions:<BR>\n" );
document.write( "1. Set up a probability distribution table for the three possible events.<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( "P(H)+P(T)+P(E) = 1\r\n" );
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document.write( "Let P(H)=P(T)=x and we are given P(E)=0.045, so\r\n" );
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document.write( "x + x + 0.045 = 1\r\n" );
document.write( "   2x + 0.045 = 1\r\n" );
document.write( "           2x = 1-0.045\r\n" );
document.write( "           2x = 0.955\r\n" );
document.write( "            x = 0.4775         \r\n" );
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document.write( "P(H) = P(T) = 0.4775   \r\n" );
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document.write( "X   P(X)\r\n" );
document.write( "----------\r\n" );
document.write( "H   0.4775 \r\n" );
document.write( "T   0.4775\r\n" );
document.write( "E   0.045\r\n" );
document.write( "----------\r\n" );
document.write( "    1.0000\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "2. If the coin were flipped twice, what would be the probability that it would<BR>\n" );
document.write( "show tails the first time and would come to rest on its edge the second time? <BR>\n" );
document.write( "Provide a brief explanation to support your computation(s). Show the probability<BR>\n" );
document.write( "value in 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" );
document.write( "Since the results of the flips are independent events, we can multiply their \r\n" );
document.write( "probabilities to find the probability that both occur.\r\n" );
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document.write( "P(H&E) = P(H)P(E) = (0.4775)(0.045) = 0.0214875, round to 0.0215\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "3. If the coin were flipped 14 times, what would be the probability that the<BR>\n" );
document.write( "coin would come to rest on its edge (“getting edge”) at most twice? Showing your<BR>\n" );
document.write( "work, report the probability value in 4 decimal places. Treat the problem as a<BR>\n" );
document.write( "binomial experiment.<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( "On your TI-84, press ON, CLEAR 2ND VARS, use down arrow key to scroll down to\r\n" );
document.write( "B:binomcdf  (the \"c\" is for \"cumulative\", there is also an A:binompdf (the \"p\"\r\n" );
document.write( "is for particular\").  You are accumulating for 0,1, or 2 E's.\r\n" );
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document.write( "Press ENTER\r\n" );
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document.write( "Make the next screen (if your calculator is a newer model) read:\r\n" );
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document.write( "    binomcdf\r\n" );
document.write( "trials:14\r\n" );
document.write( "p:0.045\r\n" );
document.write( "x value:2\r\n" );
document.write( "Paste\r\n" );
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document.write( "Use down arrow to scroll down to Paste\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "read this (or if you calculator is old, you will have to type this in yourself:\r\n" );
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document.write( "binomcdf(14,0.045,2)  \r\n" );
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document.write( "read the answer 0.9771592698\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "4. Determine the probability of getting heads between 4 to 6 times (both<BR>\n" );
document.write( "inclusive), i.e., 4 times, 5 times, or 6 times, when the coin is flipped 14<BR>\n" );
document.write( "times. Showing your work, report the probability value in 4 decimal places.<BR>\n" );
document.write( "Treat the problem as a binomial experiment.<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( "I'll leave this to you. But you have to use A:binompdf (not B:binomcdf), because\r\n" );
document.write( "you are not accumulating from 0 up to x, but want particular values of x, once\r\n" );
document.write( "with x=4, once with x=5 and once with x=6. Then add the three values you get.\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "5. What is the probability of getting “heads or tails” at least once when the<BR>\n" );
document.write( "coin is flipped 14 times? Showing your work, report the probability value in 4<BR>\n" );
document.write( "decimal places. Treat the problem as a binomial experiment<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( "This is the same as getting 'Edge' at most 1 time.  It's done the same way as\r\n" );
document.write( "problem 3 except x=1 instead of x=2.\r\n" );
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document.write( "I'll also leave this one up to you.  Good luck.\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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