document.write( "Question 1200731: 1. A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event \"shortage of A\" and F be the event \"shortage of B\". Construct a Venn diagram representing events E and F.\r
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Algebra.Com's Answer #834936 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A factory needs two raw materials.
\n" ); document.write( "The probability of not having an adequate supply of material A is 0.05, whereas
\n" ); document.write( "the probability of not having an adequate supply of material B is 0.03.
\n" ); document.write( "A study determines that the probability of a shortage in both A and B is 0.01.
\n" ); document.write( "(a) Let E be the event \"shortage of A\" and F be the event \"shortage of B\".
\n" ); document.write( "Construct a Venn diagram representing events E and F.
\n" ); document.write( "(b) Are events E and F independent explain
\n" ); document.write( "(c) What proportion of the time can the factory operate? Explain
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document.write( "We are given P(E) = P(shortage of A) = 0.05;\r\n" );
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document.write( "             P(F) = P(shortage of B) = 0.03;\r\n" );
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document.write( "             P(E and F) = P((shortage of A) AND (shortage of B)) = 0.01.\r\n" );
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document.write( "It implies  P(E)*P(F) = 0.05*0.03 = 0.0015.  Compare it with P(E and F) = 0.01.\r\n" );
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document.write( "You see that  P(E)*P(F) =/= P(E and F).  Hence, the events E and F are NOT independent.\r\n" );
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document.write( "It is the ANSWER to question (b).\r\n" );
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document.write( "Next,  P((shortage of A) OR (shortage of B)) = 0.05 + 0.03 - 0.01 = 0.07.    \r\n" );
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document.write( "It implies P(no ((shortage of A) OR (shortage of B))) = 1 - 0.07 = 0.93.    (*)     (complementary event).\r\n" );
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document.write( "According to the context, the condition that the factory operates normally is \r\n" );
document.write( "         \"no ((shortage of A) OR (shortage of B))\".\r\n" );
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document.write( "The probability of it is 0.93, according to (*).\r\n" );
document.write( "So, the factory will operate 93% of time.\r\n" );
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document.write( "It is the ANSWER to question (c).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved: questions (b) and (c) are answered.\r
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