document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196701>Question 1196701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #1 spinner circle is half green, 1/4 red and 1/4 blue.  #2 spinner circle is half red, the other half has green, red, and yellow in equal sections.<BR>\n" );
document.write( "If you get the same color twice, what is the probability it was red?  green?\r<BR>\n" );
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document.write( "Grammatically, the statement of the problem is flawed.  \"If you get the same color twice...\" implies that you are doing something twice -- e.g., spinning one of the spinners twice.  But the apparent intent of the question is that EACH spinner is spun ONCE.<br><BR>\n" );
document.write( "Overlooking that shortcoming with the statement of the problem....<br><BR>\n" );
document.write( "Only the red and green colors are on both spinners, so note that the sum of the answers to the two questions must be 1.<br><BR>\n" );
document.write( "Spinner #1 is 1/4 red; spinner #2 is (1/2+1/6) = 2/3 red.  The probability of getting red on both spinners is (1/4)(2/3) = 2/12.<br><BR>\n" );
document.write( "Spinner #1 is 1/2 green; spinner #2 is 1/6 green.  The probability of getting green on both spinners is (1/2)(1/6) = 1/12.<br><BR>\n" );
document.write( "So the probability of getting the same color on both spinners is (2/12)+(1/12) = 3/12.<br><BR>\n" );
document.write( "Then the CONDITIONAL probability that you get red on both spinners, GIVEN THAT you got the same color on both spinners, is (2/12)/(3/12) = 2/3.<br><BR>\n" );
document.write( "And the conditional probability that you get green on both spinners, given that you got the same color on both spinners, is (1/12)/(3/12) = 1/3.<br><BR>\n" );
document.write( "ANSWERS: red 2/3; green 1/3<br><BR>\n" );
document.write( "And note that the sum of the two answers is 1, as it must be....<br><BR>\n" );
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