document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200597>Question 1200597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Untitled<BR>\n" );
document.write( "Feb 24, 2023\r<BR>\n" );
document.write( "\n" );
document.write( "6. An engineering Company advertises a job in three news papers A,B,C.if it is <BR>\n" );
document.write( "known that these papers attract undergraduate engineering readerships in the <BR>\n" );
document.write( "proportions 2:3:1. The probabiity that an engineerig undergraduate sees and <BR>\n" );
document.write( "replies to the Job advertisement in the papers are 0.002, 0.001 and 0.005 <BR>\n" );
document.write( "respectively. Assume that the ungergraduate sees Only one job advertisement a) <BR>\n" );
document.write( "the ergineering company receives only one reply to it advertisements, calculate <BR>\n" );
document.write( "the probability that the applicant has seen the job adv ertised in place.<BR>\n" );
document.write( "1.a,A b,B, c,C. <BR>\n" );
document.write( "2.if the company recaives two replies, what is the probability that both <BR>\n" );
document.write( "applicants saw the jOb advertised in paper A? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848070 by </B><A HREF=/tutors/aboutme.mpl?userid=GingerAle><B>GingerAle(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=GingerAle><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's calculate the probabilities.\r<BR>\n" );
document.write( "\n" );
document.write( "**1. Probability that the applicant has seen the job advertised in paper A, given only one reply:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Define Probabilities:**<BR>\n" );
document.write( "    * Let P(A), P(B), and P(C) be the probabilities of an undergraduate seeing the ad in papers A, B, and C, respectively.<BR>\n" );
document.write( "    * Let R(A), R(B), and R(C) be the probabilities of replying to the ad in papers A, B, and C, respectively.\r<BR>\n" );
document.write( "\n" );
document.write( "* **Given:**<BR>\n" );
document.write( "    * P(A) = 2/6 = 1/3<BR>\n" );
document.write( "    * P(B) = 3/6 = 1/2<BR>\n" );
document.write( "    * P(C) = 1/6<BR>\n" );
document.write( "    * R(A) = 0.002<BR>\n" );
document.write( "    * R(B) = 0.001<BR>\n" );
document.write( "    * R(C) = 0.005\r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the probability of receiving a reply from each paper:**<BR>\n" );
document.write( "    * P(reply from A) = P(A) * R(A) = (1/3) * 0.002 = 0.000667<BR>\n" );
document.write( "    * P(reply from B) = P(B) * R(B) = (1/2) * 0.001 = 0.0005<BR>\n" );
document.write( "    * P(reply from C) = P(C) * R(C) = (1/6) * 0.005 = 0.000833\r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the probability that the applicant has seen the job advertised in paper A, given only one reply:**<BR>\n" );
document.write( "    * P(A | one reply) = P(reply from A) / (P(reply from A) + P(reply from B) + P(reply from C))<BR>\n" );
document.write( "    * P(A | one reply) = 0.000667 / (0.000667 + 0.0005 + 0.000833) <BR>\n" );
document.write( "    * P(A | one reply) = 0.000667 / 0.002 <BR>\n" );
document.write( "    * P(A | one reply) = 1/3 \r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, the probability that the applicant has seen the job advertised in paper A, given only one reply, is 1/3.**\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Probability that both applicants saw the job advertised in paper A, given two replies:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Assuming the replies are independent events:<BR>\n" );
document.write( "    * P(both replies from A) = P(reply from A) * P(reply from A)<BR>\n" );
document.write( "    * P(both replies from A) = 0.000667 * 0.000667 <BR>\n" );
document.write( "    * P(both replies from A) = 0.000000444889\r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the probability that both applicants saw the job advertised in paper A, given two replies:**<BR>\n" );
document.write( "    * P(both A | two replies) = P(both replies from A) / (P(reply from any paper) * P(reply from any paper))<BR>\n" );
document.write( "    * P(both A | two replies) = 0.000000444889 / (0.002 * 0.002) <BR>\n" );
document.write( "    * P(both A | two replies) = 0.111222222 \r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, the probability that both applicants saw the job advertised in paper A, given two replies, is approximately 0.1112.**<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );