document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036314>Question 1036314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investor invests in stocks without being informed of all the intricacies of stock market. The probability that his 1st investment in one market sector is a good stock is 1/3 and that his second investment in an unrelated market sector is a good stock is 1/4. <BR>\n" );
document.write( "Find THE probability that: \r<BR>\n" );
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document.write( "A)At least one investment would be a good stock <BR>\n" );
document.write( "B)Both the investments would be good stocks<BR>\n" );
document.write( "C) Only one investment would be a good stock <BR>\n" );
document.write( "D)None of the investments would be a good stock. \r<BR>\n" );
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document.write( "Thanks in advance!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650976 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=650976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem:\r<BR>\n" );
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document.write( "An investor invests in stocks without being informed of all the intricacies of stock market. The probability that his 1st investment in one market sector is a good stock is 1/3 and that his second investment in an unrelated market sector is a good stock is 1/4. <BR>\n" );
document.write( "Find THE probability that: <BR>\n" );
document.write( "A)At least one investment would be a good stock <BR>\n" );
document.write( "B)Both the investments would be good stocks<BR>\n" );
document.write( "C) Only one investment would be a good stock <BR>\n" );
document.write( "D)None of the investments would be a good stock. \r<BR>\n" );
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document.write( "Steps: \r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "X = event that his 1st investment is a good stock<BR>\n" );
document.write( "X' = event that his 1st investment is NOT a good stock<BR>\n" );
document.write( "Y = event that his 2nd investment is a good stock<BR>\n" );
document.write( "Y' = event that his 2nd investment is NOT a good stock\r<BR>\n" );
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document.write( "So the corresponding probabilities are<BR>\n" );
document.write( "P(X) = 1/3<BR>\n" );
document.write( "P(Y) = 1/4<BR>\n" );
document.write( "P(X') = 1 - (1/3) = 3/3 - 1/3 = 2/3<BR>\n" );
document.write( "P(Y') = 1 - (1/4) = 4/4 - 1/4 = 3/4\r<BR>\n" );
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document.write( "In short,<BR>\n" );
document.write( "P(X) = 1/3<BR>\n" );
document.write( "P(Y) = 1/4<BR>\n" );
document.write( "P(X') = 2/3<BR>\n" );
document.write( "P(Y') = 3/4\r<BR>\n" );
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document.write( "Let's move onto part (A)\r<BR>\n" );
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document.write( "(A)\r<BR>\n" );
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document.write( "The two events are independent, so we can use the rule that P(X and Y) = P(X)*P(Y)\r<BR>\n" );
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document.write( "The probability that BOTH investments are bad investments is the same as asking for the probability of event X' happening and event Y' happening as well.\r<BR>\n" );
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document.write( "P(X' and Y') = P(X')*P(Y')<BR>\n" );
document.write( "P(X' and Y') = (2/3)*(3/4)<BR>\n" );
document.write( "P(X' and Y') = (2*3)/(3*4)<BR>\n" );
document.write( "P(X' and Y') = 6/12<BR>\n" );
document.write( "P(X' and Y') = 1/2\r<BR>\n" );
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document.write( "Subtract this from 1\r<BR>\n" );
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document.write( "1 - (probability both bad) = 1 - (1/2) = 2/2 - 1/2 = 1/2\r<BR>\n" );
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document.write( "So the probability of having at least one good investment is 1/2\r<BR>\n" );
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document.write( "The final answer to part (A) is <font color=red>1/2</font>\r<BR>\n" );
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document.write( "(B)\r<BR>\n" );
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document.write( "The events X and Y are independent so P(X and Y) = P(X)*P(Y)\r<BR>\n" );
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document.write( "P(X and Y) = P(X)*P(Y)<BR>\n" );
document.write( "P(X and Y) = (1/3)*(1/4)<BR>\n" );
document.write( "P(X and Y) = (1*1)/(3*4)<BR>\n" );
document.write( "P(X and Y) = 1/12\r<BR>\n" );
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document.write( "The final answer to part B is <font color=red>1/12</font>\r<BR>\n" );
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document.write( "(C)\r<BR>\n" );
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document.write( "Add the probabilities P(X) and P(Y). Then subtract off the probability found in part (B) to get the final answer\r<BR>\n" );
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document.write( "P(X or Y) = P(X) + P(Y) - P(X and Y)\r<BR>\n" );
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document.write( "Note: when I say P(X or Y) I mean you can only pick one event (X or Y). You cannot pick both. This is an exclusive 'or'.\r<BR>\n" );
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document.write( "So using that formula gives us this\r<BR>\n" );
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document.write( "P(X or Y) = P(X) + P(Y) - P(X and Y)<BR>\n" );
document.write( "P(X or Y) = 1/3+1/4 - 1/12<BR>\n" );
document.write( "P(X or Y) = 4/12+3/12 - 1/12<BR>\n" );
document.write( "P(X or Y) = (4+3-1)/12<BR>\n" );
document.write( "P(X or Y) = 6/12<BR>\n" );
document.write( "P(X or Y) = 1/2\r<BR>\n" );
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document.write( "Answer to part C is <font color=red>1/2</font>\r<BR>\n" );
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document.write( "(D)\r<BR>\n" );
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document.write( "\"None of the investments would be a good stock\" is the same as \"Both investments are bad\"\r<BR>\n" );
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document.write( "P(X' and Y') = P(X')*P(Y')<BR>\n" );
document.write( "P(X' and Y') = (2/3)*(3/4)<BR>\n" );
document.write( "P(X' and Y') = (2*3)/(3*4)<BR>\n" );
document.write( "P(X' and Y') = 6/12<BR>\n" );
document.write( "P(X' and Y') = 1/2\r<BR>\n" );
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document.write( "Answer to part D is <font color=red>1/2</font>\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "Answer to part A: <font color=red>1/2</font><BR>\n" );
document.write( "Answer to part B: <font color=red>1/12</font><BR>\n" );
document.write( "Answer to part C: <font color=red>1/2</font><BR>\n" );
document.write( "Answer to part D: <font color=red>1/2</font>\r<BR>\n" );
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document.write( "Answers are given in fraction form. </SPAN>\n" );
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