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 #849065 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this probability problem:\r<BR>\n" );
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document.write( "First, let's organize the data into a table:\r<BR>\n" );
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document.write( "| Hotel | Lodging Only | Lodging with Breakfast | Total |<BR>\n" );
document.write( "|---|---|---|---|<BR>\n" );
document.write( "| A | 30 | 80 (110 total - 30 lodging only) | 110 |<BR>\n" );
document.write( "| B | 90 (210 total - 120 with breakfast) | 120 | 210 |<BR>\n" );
document.write( "| Total | 120 | 200 | 300 |\r<BR>\n" );
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document.write( "**(a) Probability of Hotel A or Lodging Only:**\r<BR>\n" );
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document.write( "P(A or Lodging Only) = P(A) + P(Lodging Only) - P(A and Lodging Only)<BR>\n" );
document.write( "P(A) = 110/300<BR>\n" );
document.write( "P(Lodging Only) = 120/300<BR>\n" );
document.write( "P(A and Lodging Only) = 30/300\r<BR>\n" );
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document.write( "P(A or Lodging Only) = (110/300) + (120/300) - (30/300) = 200/300 = 2/3\r<BR>\n" );
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document.write( "**(b) Probability of Hotel B with Breakfast, given Hotel B:**\r<BR>\n" );
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document.write( "This is a conditional probability. We want P(B with Breakfast | B).\r<BR>\n" );
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document.write( "P(B with Breakfast | B) = P(B with Breakfast and B) / P(B)<BR>\n" );
document.write( "Since \"B with Breakfast\" is a subset of \"B\",  P(B with Breakfast and B) = P(B with Breakfast) = 120/300<BR>\n" );
document.write( "P(B) = 210/300\r<BR>\n" );
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document.write( "P(B with Breakfast | B) = (120/300) / (210/300) = 120/210 = 4/7\r<BR>\n" );
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document.write( "**(c) Probability of Hotel A, given Lodging Only:**\r<BR>\n" );
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document.write( "This is also a conditional probability: P(A | Lodging Only)\r<BR>\n" );
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document.write( "P(A | Lodging Only) = P(A and Lodging Only) / P(Lodging Only)<BR>\n" );
document.write( "P(A and Lodging Only) = 30/300<BR>\n" );
document.write( "P(Lodging Only) = 120/300\r<BR>\n" );
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document.write( "P(A | Lodging Only) = (30/300) / (120/300) = 30/120 = 1/4\r<BR>\n" );
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document.write( "**(d) Probability of Hotel A without Breakfast or Hotel B with Breakfast:**\r<BR>\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<BR>\n" );
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document.write( "P(A without Breakfast) = 30/300<BR>\n" );
document.write( "P(B with Breakfast) = 120/300\r<BR>\n" );
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document.write( "P(A without Breakfast or B with Breakfast) = (30/300) + (120/300) = 150/300 = 1/2<BR>\n" );
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