document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033625>Question 1033625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lauren is the point guard on her basketball team. She estimates that her chances of getting a 3-pointer are 85% when there is no one defending against her, but only 60% when there is a defender. There is a 50% chance that the girl assigned to defend her will not be close enough to block the shot. What is the probability of Lauren scoring a 3-point shot? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648425 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=648425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the way i see this problem is as follows:\r<BR>\n" );
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document.write( "she has 85% probability to score the 3 pointer if the defender is not close enough to give her a hard time.\r<BR>\n" );
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document.write( "she has 60% probability to score the 3 pointer if the defender is close enough to give her a hard time.\r<BR>\n" );
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document.write( "the defender has 50% probability to be close enough to give her a hard time.\r<BR>\n" );
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document.write( "the probability that she will make the shot is therefore .5 * .85 + .5 * .60 = .725.\r<BR>\n" );
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document.write( "she will be able to score the 3 pointer 72.5% of the time overall.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume she tries 1000 times.\r<BR>\n" );
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document.write( "500 of those times the defender is close enough.<BR>\n" );
document.write( "500 of those times the defender is not close enough.\r<BR>\n" );
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document.write( "for the 500 of the times that the defender is close enough, she scores .60 * 500 = 300 times.\r<BR>\n" );
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document.write( "for the 500 of the times that the defender is not close enough, she scores .85 * 500 = 425 times.\r<BR>\n" );
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document.write( "for the 1000 times that she tries, she scores 300 + 425 = 725 times.\r<BR>\n" );
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document.write( "725 / 1000 = .725 which is the probability we originally calculated above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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