document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210436>Question 1210436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Round each answer to at least 4 decimal places accuracy.<BR>\n" );
document.write( "Owen, the inventory manager at a company's distribution center, records the following inventory for a beach towel that comes in two sizes (large or small) and three colors (Green, Black, and Yellow).<BR>\n" );
document.write( "Green  Black  Yellow Total<BR>\n" );
document.write( "Large 18 5 3 26<BR>\n" );
document.write( "Small 7 13 2 22<BR>\n" );
document.write( "Total 25 18 5 48<BR>\n" );
document.write( "a. If Owen selects one beach towel at random, what is the probability that the beach towel is Black or Yellow?<BR>\n" );
document.write( "Drive<BR>\n" );
document.write( "65<BR>\n" );
document.write( "oach<BR>\n" );
document.write( "Climate<BR>\n" );
document.write( "b. If Owen selects one beach towel at random, what is the probability that it is Small, given that it is Green?<BR>\n" );
document.write( "c. If Owen selects one beach towel at random, what is the probability that the beach towel is Black or that it is Large?<BR>\n" );
document.write( "d. If Owen selects one beach towel at random, Find P(Black)? </SPAN>\n" );
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document.write( "Round each answer to at least 4 decimal places accuracy.<BR>\n" );
document.write( "Owen, the inventory manager at a company's distribution center, records the following inventory for a beach towel <BR>\n" );
document.write( "that comes in two sizes (large or small) and three colors (Green, Black, and Yellow).\r<BR>\n" );
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document.write( "      Green  Black  Yellow  Total\r\n" );
document.write( "Large   18     5      3      26\r\n" );
document.write( "Small    7    13      2      22\r\n" );
document.write( "Total   25    18      5      48\r\n" );
document.write( "</PRE>(a) If Owen selects one beach towel at random, what is the probability that the beach towel is Black or Yellow?<BR>\n" );
document.write( "(b) If Owen selects one beach towel at random, what is the probability that it is Small, given that it is Green?<BR>\n" );
document.write( "(c) If Owen selects one beach towel at random, what is the probability that the beach towel is Black or that it is Large?<BR>\n" );
document.write( "(d) If Owen selects one beach towel at random, Find P(Black)?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  We should add the totals in columns \"Black\" and \"Yellow\", 18 + 5 = 23, and relate it\r\n" );
document.write( "     to the global total, which is 48.  We get\r\n" );
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document.write( "        P = 23/48 = 0.4792  (rounded)).\r\n" );
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document.write( "(b)  This question is about the conditional probability.\r\n" );
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document.write( "     To answer, we reduce our scope to the green towels (their number is 25, 1st column),\r\n" );
document.write( "     take the number of 'small' of them, which is 7), and relate one number to the other\r\n" );
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document.write( "        P = 7/25 = 0.28.   <<<---===  this number is not approximate: it is an exact number.\r\n" );
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document.write( "(c)  The favorable set is the union of two subsets. \r\n" );
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document.write( "         One   subset is \"Black\"  (2nd column, the total 18).\r\n" );
document.write( "         Other subset is \"Large\"  (1st line,   the total 26).\r\n" );
document.write( "         Their intersection is the cell (1,2) of 5 towels.\r\n" );
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document.write( "         So, the favorable set is  of  18 + 26 - 5 = 39 towels,  and we relate it to the global total 48\r\n" );
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document.write( "             P = 39/48 = 0.8125.    (exact value)\r\n" );
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document.write( "(d)  Here P(black) is the total of column \"Black', which is 18, related to the global total of 48\r\n" );
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document.write( "             P = 18/48 = 3/8 = 0.375  (exact value).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved in full: all questions are answered with explanations.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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