document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998790>Question 998790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two biased coins with probability of head is 0.3 on coin one and probability of head is 0.4 on coin two are tossed simultaneously. find probability of <BR>\n" );
document.write( "A.two heads<BR>\n" );
document.write( "B.coin one shows head<BR>\n" );
document.write( "C.one head<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616571 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Problem:<BR>\n" );
document.write( " <BR>\n" );
document.write( "Two biased coins are tossed simultaneously.<BR>\n" );
document.write( "Coin A has probability of 0.3 for heads, and<BR>\n" );
document.write( "coin B has probability of 0.4 for heads.<BR>\n" );
document.write( "Find<BR>\n" );
document.write( "(a) two heads<BR>\n" );
document.write( "(b) coin A shows head<BR>\n" );
document.write( "(c) one head<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( " <BR>\n" );
document.write( "Define event Ha=coin A shows heads, Hb=coin B shows heads.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(a) Two heads<BR>\n" );
document.write( "The two coins are independent of each other, so probability of both events (heads) happening is the product of the individual probabilities.<BR>\n" );
document.write( "Probability of two heads <BR>\n" );
document.write( "= P(Ha and Hb)<BR>\n" );
document.write( "= P(Ha)*P(Hb)<BR>\n" );
document.write( "= 0.3*0.4<BR>\n" );
document.write( "= 0.12<BR>\n" );
document.write( " <BR>\n" );
document.write( "(b) Coin A shows head<BR>\n" );
document.write( "This means that the outcome of coin B is immaterial, so<BR>\n" );
document.write( "P(Ha)=0.3<BR>\n" );
document.write( " <BR>\n" );
document.write( "(c) one head <BR>\n" );
document.write( "This means exactly one head, which is either <BR>\n" );
document.write( "event Ha and ~Hb  <BR>\n" );
document.write( "or<BR>\n" );
document.write( "event ~Ha and Hb.<BR>\n" );
document.write( "The two events are independent and mutually exclusive, so we can add the two probabilities.<BR>\n" );
document.write( "P(Ha and ~Hb)=0.3*(1-0.4)=0.18<BR>\n" );
document.write( "P(~Ha and Hb)=(1-0.3)*0.4=0.28<BR>\n" );
document.write( "Probability of showing exactly one head<BR>\n" );
document.write( "= 0.18+0.28<BR>\n" );
document.write( "= 0.46 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );