document.write( "Question 1179809: The
\n" ); document.write( "health department of a city routinely conducts two independent inspections of
\n" ); document.write( "each restaurant, with the restaurant passing only if both inspectors pass it.
\n" ); document.write( "Inspector A is very experienced and hence passes only 2 percent of restaurants
\n" ); document.write( "that actually do have health code violations. Inspector B is less experienced
\n" ); document.write( "and pass 7 percent of restaurants with health code violations what is the
\n" ); document.write( "probability that\r
\n" ); document.write( "\n" ); document.write( "(a) Inspector A passes a restaurant, give that inspector B has found a violation?\r
\n" ); document.write( "\n" ); document.write( "(b) Inspector B passes a restaurant with a violation given that inspector A passes it?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #850147 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The health department of a city routinely conducts two independent inspections
\n" ); document.write( "of each restaurant, with the restaurant passing only if both inspectors pass it.
\n" ); document.write( "Inspector A is very experienced and hence passes only 2 percent of restaurants
\n" ); document.write( "that actually do have health code violations. Inspector B is less experienced
\n" ); document.write( "and pass 7 percent of restaurants with health code violations what is the
\n" ); document.write( "probability that\r
\n" ); document.write( "\n" ); document.write( "(a) Inspector A passes a restaurant, give that inspector B has found a violation?\r
\n" ); document.write( "\n" ); document.write( "(b) Inspector B passes a restaurant with a violation given that inspector A passes it?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " This problem is on conditional probability.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  This question is to find the conditional probability\r\n" );
document.write( "\r\n" );
document.write( "                                             P(A passes AND B found a violation)\r\n" );
document.write( "        P(A passes | B found a violation) = --------------------------------------\r\n" );
document.write( "                                                   P(B found a violation)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     These events, (A passes) and (B found a violation) are independent, so the probability\r\n" );
document.write( "     of their intersection is the product of probabilities\r\n" );
document.write( "\r\n" );
document.write( "       P(A passes AND B found a violation) = P(A passes) * P(B found a violation) = 0.02*(1-0.07) = \r\n" );
document.write( "\r\n" );
document.write( "           = 0.02*0.93.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, the conditional probability is  P(A passes | B found a violation)) =  = 0.02.\r\n" );
document.write( "\r\n" );
document.write( "     This is the ANSWER  to question (a).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  For question (b), the logic/(the reasoning) is similar, and it leads to the solution\r\n" );
document.write( "\r\n" );
document.write( "         \r\n" );
document.write( "                                             P(B passes AND A passes)      0.07*0.02\r\n" );
document.write( "        P(B passes | A found a violation) = -------------------------- = --------------- = 0.07.\r\n" );
document.write( "                                                  P(A passes)                 0.02\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     This is the ANSWER  to question (b).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The answers are consistent with the intuitive feeling / understanding of independent events.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );