document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171674>Question 1171674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ⦁	The two-way table below gives the thousands of commuters in Massachusetts in 2015 by transportation method and one-way length of commute.<BR>\n" );
document.write( " 	Less than 15 minutes	15  -  29 minutes	30  -  44 minutes	45  -  59 minutes	60 or more minutes	Total<BR>\n" );
document.write( "Private vehicle	636	908	590	257	256	2647<BR>\n" );
document.write( "Public transportation	9	54	96	62	108	329<BR>\n" );
document.write( "Other means	115	70	23	7	7	222<BR>\n" );
document.write( "Total	760	1032	709	326	371	3198<BR>\n" );
document.write( "⦁	Find the probability that either the commuter used public transportation and/or the commuter had a commute of 60 or more minutes.                                                 (2 marks)<BR>\n" );
document.write( "⦁	Given that the commuter used public transportation, find the probability that the commuter had a commute of 60 or more minutes.                                                 (2 marks)<BR>\n" );
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document.write( "<tr><TD ></TD><TD >Less than 15 minutes</TD><TD >15 - 29 minutes</TD><TD >30 - 44 minutes</TD><TD >45 - 59 minutes</TD><TD >60 or more minutes</TD><TD >Total</TD></tr><tr><TD >Private vehicle</TD><TD >636</TD><TD >908</TD><TD >590</TD><TD >257</TD><TD >256</TD><TD >2647</TD></tr><tr><TD >Public transportation</TD><TD >9</TD><TD >54</TD><TD >96</TD><TD >62</TD><TD >108</TD><TD >329</TD></tr><tr><TD >Other means</TD><TD >115</TD><TD >70</TD><TD >23</TD><TD >7</TD><TD >7</TD><TD >222</TD></tr><tr><TD >Total</TD><TD >760</TD><TD >1032</TD><TD >709</TD><TD >326</TD><TD >371</TD><TD >3198</TD></tr>\n" );
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document.write( "Problem 1)<BR>\n" );
document.write( "Find the probability that either the commuter used public transportation and/or the commuter had a commute of 60 or more minutes. (2 marks)\r<BR>\n" );
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document.write( "Add up all the values in the \"public transportation\" row and all of the values in the \"60 or more minutes\" column:\r<BR>\n" );
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document.write( "9+54+96+62+108+256+7 = 592\r<BR>\n" );
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document.write( "note: don't add in the totals as they already account for the values listed above.\r<BR>\n" );
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document.write( "As a shortcut we could add the totals for the row and column: 329+371 = 700<BR>\n" );
document.write( "Then we subtract off 108 because it was counted twice: 700-108 = 592\r<BR>\n" );
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document.write( "Either way, there are 592 people who either took public transportation, their commute time was 60 minutes or more, or both events occurred. \r<BR>\n" );
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document.write( "Divide 592 over the grand total in the lower right corner and we get (592)/(3,198) = 0.185 approximately\r<BR>\n" );
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document.write( "Answer: Approximately 0.185\r<BR>\n" );
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document.write( "Problem 2) Given that the commuter used public transportation, find the probability that the commuter had a commute of 60 or more minutes. (2 marks)\r<BR>\n" );
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document.write( "Focus solely on the \"public transportation\" row. There are 108 people whose commute time was 60 or more minutes. There are 329 people total who took public transportation.\r<BR>\n" );
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document.write( "The probability of a commuter having a comute time of 60 or more minutes, given they took public transportation, is 108/329 = 0.328\r<BR>\n" );
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document.write( "Answer: Approximately 0.328\r<BR>\n" );
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