document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013446>Question 1013446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "I guess I am really lost, I posted a question yesterday and someone was nice enough to post an answer but I don't understand where the numbers came from.\r<BR>\n" );
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document.write( "Here was the question:<BR>\n" );
document.write( "I have the answers to the following questions but am not sure of the process to solve them. Thanks for the help.<BR>\n" );
document.write( "2 people throw a ball at the same time. One of them hits the target 55 out of 100 times, and the other one hits it 95 out of 100 times.<BR>\n" );
document.write( "What is the probability that exactly one of the throws Will hit the target?<BR>\n" );
document.write( "(answer: 91 / 200 )<BR>\n" );
document.write( "What is the probability that at least one of the throws will hit the target?<BR>\n" );
document.write( "( 391 / 400 )\r<BR>\n" );
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document.write( "Here is the answer posted:<BR>\n" );
document.write( "The probability that one only hits is (0.55)(0.05)=0.0275+ (0.45)(0.95)=0.4275<BR>\n" );
document.write( "They add up to 0.4550, or 45.5%, which is 91/200.<BR>\n" );
document.write( "At least one is 1-probability that both miss. That is 0.45*0.05=0.0225<BR>\n" );
document.write( "That is 2.25% or 2.25 per 100 or 9 per 400 that both miss. Subtract 9 from 400 and 391/400 is the probability that at least 1 will hit. \r<BR>\n" );
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document.write( "Where did .05 and .45 come from?\r<BR>\n" );
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document.write( "Thanks.<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 #629754 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "***- added<BR>\n" );
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document.write( "*** - One hits the target 55 out of 100 times.<BR>\n" );
document.write( "*** - The other 45 times he misses. Probability of missing=(45/100=0.45)<BR>\n" );
document.write( "*** - The second hits 95 out of 100 times.<BR>\n" );
document.write( "*** - The other 5 times he misses. Probability of missing=(5/100=0.05)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2 people throw a ball at the same time. One of them hits the target 55 out of 100 times, and the other one hits it 95 out of 100 times.<BR>\n" );
document.write( "What is the probability that exactly one of the throws Will hit the target?<BR>\n" );
document.write( "(answer: 91 / 200 )<BR>\n" );
document.write( "What is the probability that at least one of the throws will hit the target?<BR>\n" );
document.write( "( 391 / 400 )<BR>\n" );
document.write( "Here is the answer posted:<BR>\n" );
document.write( "The probability that one only hits is (0.55)(0.05)=0.0275+ (0.45)(0.95)=0.4275<BR>\n" );
document.write( ".<BR>\n" );
document.write( "*** - This is (probability first hits)*(second misses)+(first misses)*(second hits)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "They add up to 0.4550, or 45.5%, which is 91/200.\r<BR>\n" );
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document.write( "At least one is 1-probability that both miss. That is 0.45*0.05=0.0225<BR>\n" );
document.write( ". <BR>\n" );
document.write( "*** - This is (probability first misses)*(probability second misses) <BR>\n" );
document.write( ".<BR>\n" );
document.write( "That is 2.25% or 2.25 per 100 or 9 per 400 that both miss. Subtract 9 from 400 and 391/400 is the probability that at least 1 will hit.<BR>\n" );
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document.write( "*** - You can also calculate this (at least one hits) by:<BR>\n" );
document.write( "*** - (probability only one hits)+(probability both hit)<BR>\n" );
document.write( "*** - 0.4550+(0.95)(0.55)=0.4550+0.5225=0.9775 probability at least one will hit </SPAN>\n" );
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