document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192250>Question 1192250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hotel A and B offers 2 types of packages that include lodging only or lodging with<BR>\n" );
document.write( "breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only and<BR>\n" );
document.write( "120 tourists choose Hotel B for lodging with breakfast. Altogether 110 tourists choose to<BR>\n" );
document.write( "stay in Hotel A. A tourist is selected randomly;<BR>\n" );
document.write( "(a) What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?<BR>\n" );
document.write( "(b) What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?<BR>\n" );
document.write( "(c) What is the probability that the tourist to choose Hotel A, if he chose lodging without breakfast?<BR>\n" );
document.write( "(d) What is the probability that the tourist chose Hotel A without breakfast or choose Hotel B with breakfast?\r<BR>\n" );
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document.write( "thank you 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 #851837 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52810)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hotel A and B offers 2 types of packages that include lodging only or lodging with<BR>\n" );
document.write( "breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only <BR>\n" );
document.write( "and 120 tourists choose Hotel B for lodging with breakfast. <BR>\n" );
document.write( "Altogether 110 tourists choose to stay in Hotel A. <BR>\n" );
document.write( "A tourist is selected randomly.<BR>\n" );
document.write( "(a) What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?<BR>\n" );
document.write( "(b) What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?<BR>\n" );
document.write( "(c) What is the probability that the tourist to choose Hotel A, if he chose lodging without breakfast?<BR>\n" );
document.write( "(d) What is the probability that the tourist chose Hotel A without breakfast or choose Hotel B with breakfast?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The key to solving this problem is to make a Table showing different categories in the hotels.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;As soon as this table is complete, the rest is simple arithmetic.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In the post by @CPhill, the system, which calls himself as \"Artificial Intelligence\",\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is not able to construct the table correctly and fails the solution in every section.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Below is my correct solution.\r<BR>\n" );
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document.write( "First, let's organize the data into a table:\r\n" );
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document.write( " Hotel    Total         Lodging Only    Lodging with Breakfast  \r\n" );
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document.write( "   A    110  (given)     30 (given)       110 - 30 = 80\r\n" );
document.write( "   B   300-110 = 190    190-120 = 70       120 (given)\r\n" );
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document.write( "**(a) Probability of Hotel A or Lodging Only:**\r\n" );
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document.write( "      P(A or Lodging Only) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28110%2B70%29%2F300 ALIGN=MIDDLE  ALT=\"%28110%2B70%29%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F300 ALIGN=MIDDLE  ALT=\"180%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.6.\r\n" );
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document.write( "**(b) Probability of Hotel B with Breakfast, given Hotel B:**\r\n" );
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document.write( "       This is a conditional probability\r\n" );
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document.write( "          P(B with Breakfast | B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F190 ALIGN=MIDDLE  ALT=\"120%2F190\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F19 ALIGN=MIDDLE  ALT=\"12%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "**(c) Probability of Hotel A, given Lodging Only:**\r\n" );
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document.write( "      This is also a conditional probability: P(A | Lodging Only)\r\n" );
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document.write( "           P(A | Lodging Only) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%2830%2B70%29 ALIGN=MIDDLE  ALT=\"30%2F%2830%2B70%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F100 ALIGN=MIDDLE  ALT=\"30%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.3.\r\n" );
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document.write( "**(d) Probability of Hotel A without Breakfast or Hotel B with Breakfast:**\r\n" );
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document.write( "       These are mutually exclusive events (they can't both happen at the same time), so we can simply add their probabilities.\r\n" );
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document.write( "           P(A without Breakfast) + P(B with Breakfast) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F300+%2B+120%2F300 ALIGN=MIDDLE  ALT=\"30%2F300+%2B+120%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F300 ALIGN=MIDDLE  ALT=\"150%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.5. \r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "At this point, &nbsp;the problem is solved completely.\r<BR>\n" );
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document.write( "I am very shocked to see the level of inaccuracy, &nbsp;demonstrated by this &nbsp;\" AI \".\r<BR>\n" );
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document.write( "I also am very shocked by the style of presenting solution: &nbsp;it does not hesitate to produce wrong solution for simple problem,<BR>\n" );
document.write( "shamelessly deceives the reader many times and its major goal is to make an impression to the reader how smart the &nbsp;AI &nbsp;is.\r<BR>\n" );
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document.write( "Is it what you call &nbsp;\"the &nbsp;AI \" ?\r<BR>\n" );
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document.write( "The score, &nbsp;which I give to this system today is  the hard &nbsp;\" 2 \"  &nbsp;in the &nbsp;5-score scale.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Regarding the post by @CPhill . . . \r<BR>\n" );
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document.write( "Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.\r<BR>\n" );
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document.write( "The artificial intelligence is like a baby now. It is in the experimental stage <BR>\n" );
document.write( "of development and can make mistakes and produce nonsense without any embarrassment.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It has no feeling of shame - it is shameless.\r<BR>\n" );
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document.write( "This time, again, &nbsp;it made an error.\r<BR>\n" );
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document.write( "Although the @CPhill' solution are copy-paste &nbsp;Google &nbsp;AI solutions, &nbsp;there is one essential difference.\r<BR>\n" );
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document.write( "Every time, &nbsp;Google &nbsp;AI &nbsp;makes a note at the end of its solutions that &nbsp;Google &nbsp;AI &nbsp;is experimental<BR>\n" );
document.write( "and can make errors/mistakes.\r<BR>\n" );
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document.write( "All @CPhill' solutions are copy-paste of &nbsp;Google &nbsp;AI &nbsp;solutions, with one difference:<BR>\n" );
document.write( "@PChill never makes this notice and never says that his solutions are copy-past that of Google.<BR>\n" );
document.write( "So, he NEVER SAYS TRUTH.\r<BR>\n" );
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document.write( "Every time, &nbsp;@CPhill embarrassed to tell the truth.\r<BR>\n" );
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document.write( "But I am not embarrassing to tell the truth, &nbsp;as it is my duty at this forum.\r<BR>\n" );
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document.write( "And the last my comment.\r<BR>\n" );
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document.write( "When you obtain such posts from @CPhill, &nbsp;remember, &nbsp;that &nbsp;NOBODY &nbsp;is responsible for their correctness, <BR>\n" );
document.write( "until the specialists and experts will check and confirm their correctness.\r<BR>\n" );
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document.write( "Without it, &nbsp;their reliability is &nbsp;ZERO and their creadability is &nbsp;ZERO, &nbsp;too.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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