document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096145>Question 1096145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help. Thank you. <BR>\n" );
document.write( "A biased coin has a 70 % chance of landing on heads. The coin tossed 3 times in a row. What is probability of \"exactly 2 heads given that at least 1 head showing up. <BR>\n" );
document.write( "2 heads given is hht, hth, thh, so (0.7*0.7*0.3)*3=0.441.<BR>\n" );
document.write( "But confused with at least 1 head part. <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 #710658 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Using the format for displaying results that you show in your message....<br><BR>\n" );
document.write( "3 heads is hhh, so (0.7*0.7*0.7) = 0.343.<BR>\n" );
document.write( "2 heads given is hht, hth, thh, so (0.7*0.7*0.3)*3=0.441.<BR>\n" );
document.write( "1 heads is htt, tht, tth, so (0.7*0.3*0.3)*3 = 0.189.<BR>\n" );
document.write( "0 heads is ttt, so (0.3*0.3*0.3) = 0.027.<br><BR>\n" );
document.write( "Note that finding the probabilities of all possible cases can be good practice for a beginning student; it also gives confidence in your method and your calculations to see that the sum of the probabilities for all the cases is 1.<br><BR>\n" );
document.write( "Now.... Since the probability of no heads is 0.027, the probability of at least one head is 1-0.027 = 0.973.<br><BR>\n" );
document.write( "And when the probability question asks for the probability of getting 2 heads, GIVEN THAT THERE WAS AT LEAST 1 HEAD, it means that the sample space is only the outcomes that had at least one head; and that means the denominator of your probability fraction is the probability that there is at least one head.<br><BR>\n" );
document.write( "And finally, since the numerator is the probability of getting 2 heads, the probability fraction for the question that is being asked is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.441%2F0.973 ALIGN=MIDDLE  ALT=\"0.441%2F0.973\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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