document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179637>Question 1179637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company owns a fleet of 20 cars, each having either manual or automatic transmission and either 2 or 4 door models, and of these, 12 have automatic transmission. There are only 4 car with manual transmission . if a car is picked at radon from the fleet, calculate the probability that it is :<BR>\n" );
document.write( "a)automatic<BR>\n" );
document.write( "b)automatic or 2-door<BR>\n" );
document.write( "c)automatic and 2-door<BR>\n" );
document.write( "d)4-door<BR>\n" );
document.write( "e)automatic given that it is a 4-door car<BR>\n" );
document.write( "f) 4-door car given that it is automatic  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850205 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this probability problem step-by-step.\r<BR>\n" );
document.write( "\n" );
document.write( "**1. Define the Variables**\r<BR>\n" );
document.write( "\n" );
document.write( "* Total Cars: 20<BR>\n" );
document.write( "* Automatic Transmission (A): 12 cars<BR>\n" );
document.write( "* Manual Transmission (M): 4 cars<BR>\n" );
document.write( "* 2-Door (2D)<BR>\n" );
document.write( "* 4-Door (4D)\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Deduce Information**\r<BR>\n" );
document.write( "\n" );
document.write( "* Since there are 20 total cars, 12 automatic, and 4 manual, then 20-12-4 = 4 cars are unaccounted for. This indicates an error in the problem description. It should be 8 manual cars. However, we will solve the problem as given.\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Calculate Probabilities**\r<BR>\n" );
document.write( "\n" );
document.write( "* **a) Automatic (A)**<BR>\n" );
document.write( "    * P(A) = (Number of automatic cars) / (Total cars)<BR>\n" );
document.write( "    * P(A) = 12 / 20 = 3 / 5 = 0.6\r<BR>\n" );
document.write( "\n" );
document.write( "* **b) Automatic or 2-Door (A or 2D)**<BR>\n" );
document.write( "    * We need more information to calculate this accurately. We need to know how many 2-door cars there are, and how many of those are automatic. However, we can use the general formula:<BR>\n" );
document.write( "    * P(A or 2D) = P(A) + P(2D) - P(A and 2D)<BR>\n" );
document.write( "    * Without knowing the distribution of 2-door cars, we cannot provide an exact answer.\r<BR>\n" );
document.write( "\n" );
document.write( "* **c) Automatic and 2-Door (A and 2D)**<BR>\n" );
document.write( "    * We need the number of cars that are both automatic and 2-door. Without that information, we cannot calculate the probability.\r<BR>\n" );
document.write( "\n" );
document.write( "* **d) 4-Door (4D)**<BR>\n" );
document.write( "    * We need the number of 4-door cars to calculate this. Without that information, we cannot calculate the probability.\r<BR>\n" );
document.write( "\n" );
document.write( "* **e) Automatic given that it is a 4-Door car (A|4D)**<BR>\n" );
document.write( "    * P(A|4D) = P(A and 4D) / P(4D)<BR>\n" );
document.write( "    * We need the number of automatic 4-door cars and the total number of 4-door cars. Without that information, we cannot calculate the probability.\r<BR>\n" );
document.write( "\n" );
document.write( "* **f) 4-Door car given that it is automatic (4D|A)**<BR>\n" );
document.write( "    * P(4D|A) = P(4D and A) / P(A)<BR>\n" );
document.write( "    * We need the number of automatic 4-door cars. We know P(A) = 12/20.<BR>\n" );
document.write( "    * Without the number of automatic 4-door cars, we cannot calculate the probability.\r<BR>\n" );
document.write( "\n" );
document.write( "**To solve parts (b), (c), (d), (e), and (f), we need additional information about the distribution of 2-door and 4-door cars within the fleet.**<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );