document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=938756>Question 938756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability that a particular surgery is successful is 0.70. Find the probability that none of the four such surgeries is successful: (choose 2)<BR>\n" );
document.write( " 0.81%<BR>\n" );
document.write( " 3/7<BR>\n" );
document.write( " The events are independent from each other.<BR>\n" );
document.write( " 0.3<BR>\n" );
document.write( " The events are dependent on each other. </SPAN>\n" );
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document.write( "First we have to establish independence.<BR>\n" );
document.write( "Most of the time, the surgeries are on separate and unrelated patients, and they are not normally done by the same surgeon.  So it is a reasonable assumption that individual surgeries are independent.  Besides, there is no information on dependence, if any.<BR>\n" );
document.write( "We conclude that \"The events are independent from each other.\" is one of the choices.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Now to find the probability, we are given that <BR>\n" );
document.write( "P(success) = p = 0.70<BR>\n" );
document.write( "which leads to<BR>\n" );
document.write( "P(failure) = q = 1-p = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.70 ALIGN=MIDDLE  ALT=\"1-0.70\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.30<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Using the multiplication rule, which says that the probability of multi-step events which are independent is the product of the individual probabilities.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "P(4 failures) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E4 ALIGN=MIDDLE  ALT=\"q%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.3%5E4+ ALIGN=MIDDLE  ALT=\"+0.3%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0081 = 0.81%<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Answer: probability of 4 unsuccessful surgeries is 0.81%<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );