document.write( "Question 1206108: In a large city, 37% of all restaurants accept both master and visa credit cards, and 50% accept master cards and 60% accept visa cards. A tourist visiting the city picks at random a restaurant at which to have lunch. Define the following events:
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\n" ); document.write( "\n" ); document.write( "1)Are M and V disjoint?
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\n" ); document.write( "3 Is M complement of V
\n" ); document.write( "4.What is the probability that a given restaurant does not accept master or visa credit cards?
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Algebra.Com's Answer #843339 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "In a large city, 37% of all restaurants accept both master and visa credit cards,
\n" ); document.write( "and 50% accept master cards and 60% accept visa cards. A tourist visiting the city
\n" ); document.write( "picks at random a restaurant at which to have lunch. Define the following events:
\n" ); document.write( "M= {the randomly chosen restaurant accepts master credit cards},
\n" ); document.write( "V= {the randomly chosen restaurant accepts visa credit cards}.\r
\n" ); document.write( "\n" ); document.write( "1) Are M and V disjoint?
\n" ); document.write( "2) Are M AND V independent?
\n" ); document.write( "3) Is M complement of V
\n" ); document.write( "4) What is the probability that a given restaurant does not accept master or visa credit cards?
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document.write( "(1)  The events (the sets) M and V have non-empty intersection of 37%.\r\n" );
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document.write( "     Hence, they are NOT disjoint.\r\n" );
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document.write( "(2)  To check if M and V indepentdent, we should check if P(M and V) is equal to P(M)*P(V).\r\n" );
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document.write( "     We have P(M and V) = 0.37 (given).  We also have P(M)*P(V) = 0.5*0.6 = 0.3.\r\n" );
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document.write( "     Since 0.37 =/= 0.3, we conclude that events M and V are not independent.\r\n" );
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document.write( "(3)  To check if M is complement of V, we should check TWO statements.\r\n" );
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document.write( "     (a) whether M and V are disjoint ?  - the answer is NO, see n.1 above\r\n" );
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document.write( "     (b) whether P(M) + P(V) = 1 ?       - Since 0.5 + 0.6 =/= 1, the answer is NO.\r\n" );
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document.write( "     Having at least one NO answer of these two, (a) and (b), is just enought to say\r\n" );
document.write( "     that events M and V are not complementary.\r\n" );
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document.write( "(4)  The probability that at least one restaurant accept M or V is\r\n" );
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document.write( "         P(M or V) = P(M) + P(V) - P(M and V) = 0.5 + 0.6 - 0.37 = 0.73.\r\n" );
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document.write( "     The probability that a given restaurant does not accept master or visa credit cards\r\n" );
document.write( "     is the complement to this value of 0.73.\r\n" );
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document.write( "     So, the ANSWER  to (4) is 1-0.73 = 0.27.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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