document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204607>Question 1204607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of people who survived the Titanic based on class and sex is in the table (\"Encyclopedia Titanica,\" 2013). Suppose a person is picked at random from the survivors. Round your answers to four decimals, if necessary.\r<BR>\n" );
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document.write( "ass	Sex	Total<BR>\n" );
document.write( "Female	Male<BR>\n" );
document.write( "1st	134	59	193<BR>\n" );
document.write( "2nd	94	25	119<BR>\n" );
document.write( "3rd	80	58	138<BR>\n" );
document.write( "Total	308	142	450\r<BR>\n" );
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document.write( "What is the probability that a survivor was male?<BR>\n" );
document.write( "P(male) = \r<BR>\n" );
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document.write( "What is the probability that a survivor was in the third class?<BR>\n" );
document.write( "P(third class) = \r<BR>\n" );
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document.write( "What is the probability that a survivor was a male given that the person was in third class?<BR>\n" );
document.write( "P(male|third class) = \r<BR>\n" );
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document.write( "What is the probability that a survivor was a male and in the third class?<BR>\n" );
document.write( "P(male and third class) = \r<BR>\n" );
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document.write( "What is the probability that a survivor was a male or in the third class?<BR>\n" );
document.write( "P(male or third class) = \r<BR>\n" );
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document.write( "Are the events survivor is a male and survivor is in third class mutually exclusive? Why or why not?\r<BR>\n" );
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document.write( "No, male and being in third class are not mutually exclusive, since a survivor cannot be both.<BR>\n" );
document.write( "Yes, male and being in third class are mutually exclusive, since a survivor cannot be both.<BR>\n" );
document.write( "No, male and being in third class are not mutually exclusive, since a survivor can be both.<BR>\n" );
document.write( "Yes, male and being in third class are mutually exclusive, since a survivor can be both.<BR>\n" );
document.write( "Are the events survivor is a male and survivor is in third class independent? Why or why not?\r<BR>\n" );
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document.write( "No, male and being in third class are not independent, since P(male|third class) ≠ P(male).<BR>\n" );
document.write( "Yes, male and being in third class are independent, since P(male|third class) ≠ P(male).<BR>\n" );
document.write( "Yes, male and being in third class are independent, since P(male|third class) = P(male).<BR>\n" );
document.write( "No, male and being in third class are not independent, since P(male|third class) = P(male).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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document.write( "<tr><TD ></TD><TD >Female</TD><TD >Male</TD><TD >Total</TD></tr><tr><TD >1st class</TD><TD >134</TD><TD >59</TD><TD >193</TD></tr><tr><TD >2nd class</TD><TD >94</TD><TD >25</TD><TD >119</TD></tr><tr><TD >3rd class</TD><TD >80</TD><TD >58</TD><TD >138</TD></tr><tr><TD >Total</TD><TD >308</TD><TD >142</TD><TD >450</TD></tr>\n" );
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document.write( "There are 142 males out of 450 survivors.<BR>\n" );
document.write( "P(male) = 142/450 = <font color=red>0.3156</font> approximately.\r<BR>\n" );
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document.write( "There are 138 people in 3rd class out of 450 survivors total.<BR>\n" );
document.write( "P(3rd class) = 138/450 = <font color=red>0.3067</font> approximately\r<BR>\n" );
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document.write( "Of the 138 people in 3rd class, 80 are male<BR>\n" );
document.write( "P(male given 3rd class) = 80/138 = <font color=red>0.5797</font><BR>\n" );
document.write( "Many textbooks use a vertical line to represent the key term \"given\"<BR>\n" );
document.write( "P(A | B) = P(A given B)<BR>\n" );
document.write( "I prefer using the word \"given\" to avoid confusing the vertical bar with perhaps the numeric digit one, the lowercase letter L, or the uppercase letter i.\r<BR>\n" );
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document.write( "There are 80 male survivors who are in 3rd class out of 450 total survivors.<BR>\n" );
document.write( "P(male and 3rd class) = 80/450 = <font color=red>0.1778</font> approximately<BR>\n" );
document.write( "Be careful not to mix this up with the previous probability.\r<BR>\n" );
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document.write( "Use the inclusion-exclusion principle to compute the following<BR>\n" );
document.write( "P(male or 3rd class) = P(male) + P(3rd class) - P(male and 3rd class)<BR>\n" );
document.write( "P(male or 3rd class) = (142/450) + (138/450) - (80/450)<BR>\n" );
document.write( "P(male or 3rd class) = (142+138-80)/450<BR>\n" );
document.write( "P(male or 3rd class) = 200/450<BR>\n" );
document.write( "P(male or 3rd class) = <font color=red>0.4444</font> approximately.\r<BR>\n" );
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document.write( "The events \"male\" and \"3rd class\" are NOT mutually exclusive because it is possible for both events to happen at the same time. It's possible for a survivor to be both male and be in 3rd class.<BR>\n" );
document.write( "Notice how P(male and 3rd class) is nonzero.\r<BR>\n" );
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document.write( "Compare the following probability values<BR>\n" );
document.write( "P(male given 3rd class) = 0.5797<BR>\n" );
document.write( "P(male) = 0.3156<BR>\n" );
document.write( "This leads to P(male given 3rd class) ≠ P(male), which leads us to conclude the events \"male\" and \"3rd class\" are NOT independent.<BR>\n" );
document.write( "The two events are linked somehow. We consider them dependent.<BR>\n" );
document.write( "Having prior knowledge of event \"3rd class\" changes the probability value of P(male).\r<BR>\n" );
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document.write( "Summary<ul><li>P(male) = <font color=red>0.3156</font></li><li>P(3rd class) = <font color=red>0.3067</font></li><li>P(male given 3rd class) = <font color=red>0.5797</font></li><li>P(male and 3rd class) = <font color=red>0.1778</font></li><li>P(male or 3rd class) = <font color=red>0.4444</font></li><li>male and 3rd class mutually exclusive? <font color=red>No</font>, male and being in third class are not mutually exclusive, since a survivor can be both.</li><li>male and 3rd class independent? <font color=red>No</font>, male and being in third class are not independent, since P(male given 3rd class) ≠ P(male)</li></ul>The decimal values are approximate.<BR>\n" );
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