document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409490>Question 409490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) a boy and a girl have to toss a coin . The winner is who gets the head . If the girl starts first , what's the probability the boy wins ?\r<BR>\n" );
document.write( "\n" );
document.write( "2) In a factory three new machines A,B,C have the probability of producing  <BR>\n" );
document.write( "   faulty lamps as 0.9 , 0.7 and 0.6 respectively . If three lamps<BR>\n" );
document.write( "   are selected randomly find the probabilty that at least two lamps  <BR>\n" );
document.write( "   are produced by the machine B ?<BR>\n" );
document.write( "3) Three new computers have the probability of failure as 0.75 , 0.65 and 0.5 . What's the probabilty that two computers fail in the first year ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288398 by </B><A HREF=/tutors/aboutme.mpl?userid=sudhanshu_kmr><B>sudhanshu_kmr(1152)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sudhanshu_kmr><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=sudhanshu_kmr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=288398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)\r<BR>\n" );
document.write( "\n" );
document.write( "As here the girl starts first, she can win on first, third, fifth ... toss\r<BR>\n" );
document.write( "\n" );
document.write( " probability of win on first chance  = 1/2\r<BR>\n" );
document.write( "\n" );
document.write( "probability that she can win on  second chance(i.e third toss) = 1/2*1/2*1/2\r<BR>\n" );
document.write( "\n" );
document.write( "(for win on second chance outcome should be Tail, Tail  then Head )\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "similarly probability on third chance = (1/2)^5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability the girl win  <BR>\n" );
document.write( " P(A)= 1/2 + (1/2)^3 + (1/2)^5 .............to infinity\r<BR>\n" );
document.write( "\n" );
document.write( "{ here sum of geometric progression , a = 1/2  and r = 1/4 }\r<BR>\n" );
document.write( "\n" );
document.write( " = 1/2 /[1 -1/4]\r<BR>\n" );
document.write( "\n" );
document.write( "= 2/3 \r<BR>\n" );
document.write( "\n" );
document.write( "probability the boy win = P(A') = 1-P(A) = 1/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2) \r<BR>\n" );
document.write( "\n" );
document.write( "three lamps can be faulty by following ways...\r<BR>\n" );
document.write( "\n" );
document.write( "A B C   Probability\r<BR>\n" );
document.write( "\n" );
document.write( "1 1 1 -   9/10 * 7/10* 6/10  = 378/1000\r<BR>\n" );
document.write( "\n" );
document.write( "2 1 0 -   9/10 * 9/10 * 7/10 = 567/1000<BR>\n" );
document.write( "                            <BR>\n" );
document.write( "2 0 1 -  9/10 * 9/10 * 6/10  = 486/1000\r<BR>\n" );
document.write( "\n" );
document.write( "3 0 0 -  9/10 * 9/10 * 9/10  = 729/1000\r<BR>\n" );
document.write( "\n" );
document.write( "1 2 0 -   441/1000   ( favorable condition)\r<BR>\n" );
document.write( "\n" );
document.write( "0 2 1 -   294/1000   ( favourable condition)\r<BR>\n" );
document.write( "\n" );
document.write( "0 3 0 -   343/1000    ( favourable condition)\r<BR>\n" );
document.write( "\n" );
document.write( "1 0 2 -  324/1000\r<BR>\n" );
document.write( "\n" );
document.write( "0 1 2-    252/1000\r<BR>\n" );
document.write( "\n" );
document.write( "0 0 3-   216/1000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using Bye's theory \r<BR>\n" );
document.write( "\n" );
document.write( "P(a) =   probability of favorable condition/ probability of total condition\r<BR>\n" );
document.write( "\n" );
document.write( " =  [ 441/1000  + 294/ 1000+ 343/1000]/ [ 378/1000 + .......+ 216/1000]\r<BR>\n" );
document.write( "\n" );
document.write( " =    1078 / 4030 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3)\r<BR>\n" );
document.write( "\n" );
document.write( "two computers may fail by following ways...\r<BR>\n" );
document.write( "\n" );
document.write( "probability :  A and B not C = 75/100 * 65/100 * (1- 50/100) \r<BR>\n" );
document.write( "\n" );
document.write( "A and C not B =  75/100 * 50/100 * 35/100\r<BR>\n" );
document.write( "\n" );
document.write( "B and C not A =  65/100 * 50/100 * 25/100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability that two computers fail =  [243750 +131250 + 81250 ] /1000000\r<BR>\n" );
document.write( "\n" );
document.write( "= 456250/1000000\r<BR>\n" );
document.write( "\n" );
document.write( "= 0.456250\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );