document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159728>Question 1159728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4)Suppose the probability that a bit transmitted through a digital communication channel and received in error is 0.01. Assuming that the transmissions are independent events, <BR>\n" );
document.write( "a) Find the probability that the first error occurs at the 8th bit.<BR>\n" );
document.write( "b) Find the probability that the third error occurs at the 8th bit.<BR>\n" );
document.write( "c) Find the probability that three or more errors occur among 100 transmitted bits. </SPAN>\n" );
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document.write( "probability is 0.99^7*0.01=0.0093\r<BR>\n" );
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document.write( "For the next part, we need the probability of 2 errors in 7 bits<BR>\n" );
document.write( "there are 7C2 or 21 ways that can happen and the probability to get 2 errors is 21*0.99^5*0.01^2=0.00200 or 0.002<BR>\n" );
document.write( "Then the eighth bit has a 0.01 probability of an error, so the joint probability is 0.0002 for the third error to occur on the 8th bit.\r<BR>\n" );
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document.write( "Find the probability of 0,1,2 errors among 100 bits<BR>\n" );
document.write( "for 0, it is 0.99^100=0.3660<BR>\n" );
document.write( "for 1 it is 100*0.99^99*0.01=0.3697<BR>\n" );
document.write( "for 2 it is 100C2*0.99*98*0.01^2=0.1849<BR>\n" );
document.write( "That sum is 0.9206<BR>\n" );
document.write( "Also 2nd VARS to binomcdf (100,0.01,2)<BR>\n" );
document.write( "BUT this is the probability we don't want.  The complement, 3 or more errors, is 0.0794, and that is the answer. </SPAN>\n" );
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