document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185738>Question 1185738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following table represents the age of drivers (in years) and the major causes of 944 car accidents.\r<BR>\n" );
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document.write( "Age	      Speeding	    Careless	Drinking and Driving	        Total<BR>\n" );
document.write( "Below 25	 160	   89	         286	                         535<BR>\n" );
document.write( "25 and above	 136	   219	         54	                         409<BR>\n" );
document.write( "Total	         296	   308	         340	                          944\r<BR>\n" );
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document.write( "(a) Find the probability that a randomly chosen car accident is caused by a careless driver under 25 years old. <BR>\n" );
document.write( "0.5667\r<BR>\n" );
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document.write( "(b) Find the probability that a randomly chosen car accident is caused by either drinking and driving or speeding. \r<BR>\n" );
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document.write( "(c) Find the probability that a randomly chosen car accident is caused by either drinking and driving or a driver under 25 years old. \r<BR>\n" );
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document.write( "(d) Given that a car accident was caused by speeding, calculate the probability that the driver was at least 25 years old. \r<BR>\n" );
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document.write( "(e) If two car accidents are randomly chosen (without replacement), calculate the probability that they are both caused by careless driving.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849617 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=849617\">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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