document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=338312>Question 338312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PROBABILITY:<BR>\n" );
document.write( "Choose one of the outcomes listed above.  Based on the sample space above, what is the theoretical probability that the outcome will occur? (write the probability as a fraction and as a decimal.)\r<BR>\n" );
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document.write( "Outcome:______TT3______	Probability: _____1/24 ; 0.0417______\r<BR>\n" );
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document.write( "(over)<BR>\n" );
document.write( "EXPERIMENTAL (Empirical) PROBABILITY:<BR>\n" );
document.write( "Using the same outcome you chose at the bottom of the previous page, conduct the experiment and record the number of times the outcome occurs.\r<BR>\n" );
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document.write( "Outcome: ______________\r<BR>\n" );
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document.write( "In the table below, “success” means that the above outcome occurred.  You will conduct the experiment a total of 100 times.\r<BR>\n" );
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document.write( "	# of successes for this set of 10 trials	Cumulative number of successes	Proportion of successes based on all trials	Decimal estimate of successes based on all trials<BR>\n" );
document.write( "First set of 10 trials			/10	<BR>\n" );
document.write( "Second set of 10 trials			/20	<BR>\n" );
document.write( "Third set of 10 trials			/30	<BR>\n" );
document.write( "Fourth set of 10 trials			/40	<BR>\n" );
document.write( "Fifth set of 10 trials			/50	<BR>\n" );
document.write( "Sixth set of 10 trials			/60	<BR>\n" );
document.write( "Seventh set of 10 trials			/70	<BR>\n" );
document.write( "Eighth set of 10 trials			/80	<BR>\n" );
document.write( "Ninth set of 10 trials			/90	<BR>\n" );
document.write( "Tenth set of 10 trials			/100	\r<BR>\n" );
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document.write( "Look at the far right column of the table.  How does the empirical probability compare to the theoretical probability as the total number of trials increases?  What would happen to the numbers in the far right column if you repeated the experiment 1000 times?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #242549 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=242549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PROBABILITY:<BR>\n" );
document.write( "Choose one of the outcomes listed above. Based on the sample space above, what is the theoretical probability that the outcome will occur? (write the probability as a fraction and as a decimal.) \r<BR>\n" );
document.write( "\n" );
document.write( "Outcome:______TT3______ Probability: _____1/24 ; 0.0417______ \r<BR>\n" );
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document.write( "(over)<BR>\n" );
document.write( "EXPERIMENTAL (Empirical) PROBABILITY:<BR>\n" );
document.write( "Using the same outcome you chose at the bottom of the previous page, conduct the experiment and record the number of times the outcome occurs.<BR>\n" );
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document.write( "Comment: This tells you to flip the coin one, then flip it again, then<BR>\n" );
document.write( "roll a dice once.  That would constitute one trial of the experiment.<BR>\n" );
document.write( "Let's assume you perform the experiment 24 times.<BR>\n" );
document.write( "You are to keep track of how many time tt3 occurs and record that <BR>\n" );
document.write( "number below.<BR>\n" );
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document.write( "Outcome: put your number here______________ <BR>\n" );
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document.write( "In the table below, “success” means that the above outcome occurred.<BR>\n" );
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document.write( "You will conduct the experiment a total of 100 times. <BR>\n" );
document.write( "# of successes for each set of 10 trials <BR>\n" );
document.write( "Cumulative number of successes <BR>\n" );
document.write( "Proportion of successes based on all trials <BR>\n" );
document.write( "Decimal estimate of successes based on all trials<BR>\n" );
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document.write( "Comment: Now you are perform the experiment 10 times and list the number of tt3.<BR>\n" );
document.write( "Do it again for 10 trials.<BR>\n" );
document.write( "And again<BR>\n" );
document.write( "And again<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "Add up the number of successes as you go through each set of 10 trials.<BR>\n" );
document.write( "First set of 10 trials /10 <BR>\n" );
document.write( "Second set of 10 trials /20 <BR>\n" );
document.write( "Third set of 10 trials /30 <BR>\n" );
document.write( "Fourth set of 10 trials /40 <BR>\n" );
document.write( "Fifth set of 10 trials /50 <BR>\n" );
document.write( "Sixth set of 10 trials /60 <BR>\n" );
document.write( "Seventh set of 10 trials /70 <BR>\n" );
document.write( "Eighth set of 10 trials /80 <BR>\n" );
document.write( "Ninth set of 10 trials /90 <BR>\n" );
document.write( "Tenth set of 10 trials /100 \r<BR>\n" );
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document.write( "Look at the far right column of the table.<BR>\n" );
document.write( "Comment: The far right column contains the cumulative sum of the decimal equivalents of the number of tt3's as you perform the trial more and more times.\r<BR>\n" );
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document.write( "How does the empirical probability compare to the theoretical probability as the total number of trials increases? What would happen to the numbers in the far right column if you repeated the experiment 1000 times?<BR>\n" );
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document.write( "Comment: As you increase the number of trials the emperical proportion of <BR>\n" );
document.write( "tt3 results will get closer and closer to the theoretical proportion of <BR>\n" );
document.write( "1 out of 24 = 0.0417<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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