document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196340>Question 1196340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a fair coin is tossed five times what is the probability that the number of times you observe H is a prime number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829130 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "List of primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...} <BR>\n" );
document.write( "The value 1 is NOT prime.\r<BR>\n" );
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document.write( "We can trim that list down to {2,3,5} since the coin is tossed five times.\r<BR>\n" );
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document.write( "Your teacher is asking:<BR>\n" );
document.write( "(1) What is the probability of seeing exactly 2 heads?<BR>\n" );
document.write( "(2) What is the probability of seeing exactly 3 heads?<BR>\n" );
document.write( "(3) What is the probability of seeing exactly 5 heads?\r<BR>\n" );
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document.write( "I'll show you how to answer question (1), and leave the rest for you to do on your own\r<BR>\n" );
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document.write( "p = 1/2 = 0.5 = probability of getting heads<BR>\n" );
document.write( "n = 5 = number of coin tosses<BR>\n" );
document.write( "x = 2 = number of heads we wish to see<BR>\n" );
document.write( "B(x) = binomial probability function<BR>\n" );
document.write( "B(x) = (n C x)*(p^x)*(1-p)^(n-x)<BR>\n" );
document.write( "B(x) = (5 C x)*(0.5^x)*(1-0.5)^(5-x)<BR>\n" );
document.write( "B(2) = (5 C 2)*(0.5^2)*(1-0.5)^(5-2)<BR>\n" );
document.write( "B(2) = (10)*(0.5^2)*(1-0.5)^(5-2) ........... see note below<BR>\n" );
document.write( "B(2) = 0.3125<BR>\n" );
document.write( "The result is exact without any rounding done to it.\r<BR>\n" );
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document.write( "note: The n C x refers to the nCr combination formula <BR>\n" );
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document.write( "You could use the formula to compute that value, or refer to Pascal's Triangle\r<BR>\n" );
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document.write( "So B(2) = 0.3125 says we have exactly a 31.25% chance of getting exactly 2 heads out of 5 tosses.<BR>\n" );
document.write( "I'll leave the computations of B(3) and B(5) up to you to perform. <BR>\n" );
document.write( "Many calculators and spreadsheets have capabilities to quickly compute binomial probabilities, so I recommend you use them to check your work. GeoGebra is one tool I use all the time. \r<BR>\n" );
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document.write( "Once you've determined B(2), B(3) and B(5), you'll add up those values to get the final answer. <BR>\n" );
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