document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185737>Question 1185737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following data represents the information on the ratings of a random sample of 152 movies that were released last year and are classified by their genre.\r<BR>\n" );
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document.write( "Ratings	<BR>\n" );
document.write( "Genre	PG	PG-13	R	Total<BR>\n" );
document.write( "Action	2	15	17	34<BR>\n" );
document.write( "Comedy	16	11	18	45<BR>\n" );
document.write( "Drama	7	16	20	43<BR>\n" );
document.write( "Thriller20	6	4	30<BR>\n" );
document.write( "Total	45	48	59	152\r<BR>\n" );
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document.write( "(a) What is the probability that the movie is a thriller and it is rated R? <BR>\n" );
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document.write( "(b) What is the probability that the movies is either a comedy or it is rated PG-13? <BR>\n" );
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document.write( "(c) Given that the movie is an action movie, what is the probability that it is rated as PG? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849618 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</B></A><img src=\"/images/stars/stars-13.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=849618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's the breakdown of how to calculate the probabilities:\r<BR>\n" );
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document.write( "**(a) Probability of a careless driver under 25:**\r<BR>\n" );
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document.write( "*   Number of accidents caused by careless drivers under 25: 89<BR>\n" );
document.write( "*   Total number of accidents: 944<BR>\n" );
document.write( "*   Probability = (Number of careless drivers under 25) / (Total accidents) = 89 / 944 ≈ 0.0943  (Your provided answer of 0.5667 is incorrect.)\r<BR>\n" );
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document.write( "**(b) Probability of drinking and driving OR speeding:**\r<BR>\n" );
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document.write( "*   Number of accidents caused by drinking and driving: 340<BR>\n" );
document.write( "*   Number of accidents caused by speeding: 296<BR>\n" );
document.write( "*   Total accidents: 944<BR>\n" );
document.write( "*   Probability = (Drinking and driving + Speeding) / Total = (340 + 296) / 944 = 636 / 944 ≈ 0.6737\r<BR>\n" );
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document.write( "**(c) Probability of drinking and driving OR a driver under 25:**\r<BR>\n" );
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document.write( "*   Number of accidents caused by drinking and driving: 340<BR>\n" );
document.write( "*   Number of accidents involving drivers under 25: 535<BR>\n" );
document.write( "*   Number of accidents caused by drinking and driving *and* a driver under 25: 286<BR>\n" );
document.write( "*   Probability = (Drinking and driving + Under 25 - Both) / Total = (340 + 535 - 286) / 944 = 589 / 944 ≈ 0.6239\r<BR>\n" );
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document.write( "**(d) Probability the driver was at least 25 GIVEN speeding:**\r<BR>\n" );
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document.write( "*   Number of accidents caused by speeding: 296<BR>\n" );
document.write( "*   Number of accidents caused by speeding and a driver 25 or above: 136<BR>\n" );
document.write( "*   Probability = (Speeding and 25 or above) / (Total speeding) = 136 / 296 ≈ 0.4595\r<BR>\n" );
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document.write( "**(e) Probability of two careless driving accidents (without replacement):**\r<BR>\n" );
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document.write( "*   Probability of the first accident being caused by careless driving: 308 / 944<BR>\n" );
document.write( "*   After one accident is chosen, there are 943 accidents left, and 307 are caused by careless driving.<BR>\n" );
document.write( "*   Probability of the second accident being caused by careless driving: 307 / 943<BR>\n" );
document.write( "*   Probability of both being caused by careless driving = (308 / 944) * (307 / 943) ≈ 0.1066<BR>\n" );
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