document.write( "Question 1167318: The probability of snow falling on a typical day of December is .10 and the probability of a traffic jam is .80. The probability of snow or a traffic jam is .82. Are the events \"it snows\" and \"a traffic jam occurs\" independent \n" ); document.write( "

Algebra.Com's Answer #791933 by ikleyn(52848) $\"\"$ $\"About$

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document.write( "From the basic formula of the elementary probability formula\r\n" );
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document.write( "    P(snow OR a traffic jam) = P(snow) + P(a traffic jam) - P(snow AND a traffic jam).     (1)\r\n" );
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document.write( "Substitute the given data into this formula.  You will get\r\n" );
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document.write( "    0.82 = 0.8 + 0.10 - P(snow AND a traffic jam).          (2)\r\n" );
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document.write( "From this equation\r\n" );
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document.write( "    P(snow AND a traffic jam) = 0.8 + 0.1 - 0.82 = 0.08.    (3)\r\n" );
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document.write( "From the other hand side,\r\n" );
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document.write( "   P(snow) * P(a traffic jam) = 0.1 * 0.8 = 0.08.           (4)\r\n" );
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document.write( "From (3) and (4),  we see that  \r\n" );
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document.write( "    P(snow AND a traffic jam) = P(snow) * P(a traffic jam).\r\n" );
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document.write( "From the definition of independent events, it means tha the events  \"it snows\" and \"a traffic jam occurs\" independent.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lesson\r
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