document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1070398>Question 1070398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the given pair of events A and&#8203; B, complete parts&#8203; (a) and&#8203; (b) below. <BR>\n" );
document.write( "&#8203;A: A marble is randomly selected from a bag containing 2020 marbles consisting of  1&#8203; red, 1616 &#8203;blue, and 33 green marbles. The selected marble is one of the green marbles.<BR>\n" );
document.write( "&#8203;B: A second marble is selected and it is the 1 red marble in the bag.<BR>\n" );
document.write( "a. Determine whether events A and B are independent or dependent.&#8203; (If two events are technically dependent but can be treated as if they are independent according to the&#8203; 5% guideline, consider them to be&#8203; independent.)<BR>\n" );
document.write( "b. Find&#8203; P(A and&#8203; B), the probability that events A and B both occur.<BR>\n" );
document.write( "a. Choose the correct answer below.<BR>\n" );
document.write( "A.<BR>\n" );
document.write( "The two events are independent because the&#8203; 5% guideline can be applied in this case.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the&#8203; 5% guideline cannot be applied in this case.<BR>\n" );
document.write( "Your answer is correct.C.<BR>\n" );
document.write( "The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.<BR>\n" );
document.write( "D.<BR>\n" );
document.write( "The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the&#8203; 5% guideline can be applied in this case.<BR>\n" );
document.write( "b. The probability that events A and B both occur is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #685520 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=685520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The two events are technically dependent but are treated as independent because 33<5% of 2020. Picking the green marble for all practical purposes does not affect the chances of picking a red marble.<BR>\n" );
document.write( "The joint probability is 33/2020 (I assume there are other marbles in the bag)*(1/2019)<BR>\n" );
document.write( "=8.09 x 10^(-6)<BR>\n" );
document.write( "A.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );