document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022186>Question 1022186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability of a shooter hitting a target is 2/3. How many minimum numbers of times must he fire so that the probability of hitting the target at least is more than 0.98? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #637933 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=637933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the probability of hitting the target is 2/3, then the probability of missing the target is 1/3.\r<BR>\n" );
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document.write( "the probability missing one time is 1/3.<BR>\n" );
document.write( "the probability of missing two times is 1/3 * 1/3 = 1/9<BR>\n" );
document.write( "the probability of missing three times is 1/3 * 1/3 * 1/3 = 1/27<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "if you want the probability of  hitting the target to be at least .98, then the probability of missing the target has to be at most .02.\r<BR>\n" );
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document.write( "you are therefore looking for a probaiblity of missing that is less than .02.\r<BR>\n" );
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document.write( "it looks like he would have to shoot at least 4 times.\r<BR>\n" );
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document.write( "that's because 1/3 * 1/3 * 1/3 = 1/27 which is equal to .037...\r<BR>\n" );
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document.write( "multiply that by 1/3 again and you get .012... which is less than .02.\r<BR>\n" );
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document.write( "the probability of hitting the target at least one of those times has to be greater than .98.\r<BR>\n" );
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document.write( "what is the probability of hitting the target at least one out of 4 times?\r<BR>\n" );
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document.write( "that would be based on the binomial probability equation of p(x) = c(n,x) * p^x * q^(n-x).\r<BR>\n" );
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document.write( "n is the total amount of trials which is 4.<BR>\n" );
document.write( "x is the number of times you want success.<BR>\n" );
document.write( "n-x is the number of time you don't get success (you fail).<BR>\n" );
document.write( "c(n,x) is the number of ways you can get sets of x out of n elements.\r<BR>\n" );
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document.write( "the following chart shows the calculations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/022701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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