document.write( "Question 1183059: An item produced by a company is susceptible to two types
\n" ); document.write( "of defects namely, A and B. The probability that an
\n" ); document.write( "item has defect A is 0.167\r
\n" ); document.write( "\n" ); document.write( ". The probability that it has defect
\n" ); document.write( "B is 0.125
\n" ); document.write( ". Calculate the probability that the item has
\n" ); document.write( "(i) Both A and B defects
\n" ); document.write( "(ii) Only defect A
\n" ); document.write( "(iii) Only defect B
\n" ); document.write( "(iv) One defect only
\n" ); document.write( "(v) At least one defect \n" ); document.write( "
Algebra.Com's Answer #813210 by ikleyn(52810)\"\" \"About 
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\n" ); document.write( "An item produced by a company is susceptible to two types of defects namely, A and B.
\n" ); document.write( "The probability that an item has defect A is 0.167.
\n" ); document.write( "The probability that it has defect B is 0.125.
\n" ); document.write( "Calculate the probability that the item has
\n" ); document.write( "(i) Both A and B defects
\n" ); document.write( "(ii) Only defect A
\n" ); document.write( "(iii) Only defect B
\n" ); document.write( "(iv) One defect only
\n" ); document.write( "(v) At least one defect
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\n" ); document.write( "\n" ); document.write( "            From the context,  I will assume that events  A  and  B  are independent.\r
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\n" ); document.write( "\n" ); document.write( "            The problem is silent about it  (which is a deficiency of the post), \r
\n" ); document.write( "\n" ); document.write( "            but without this assumption,  the problem can not be solved/answered.\r
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document.write( "(i)    Both A and B defects  P(A and B) = P(A)*P(B) = 0.167*0.125 = 0.020875.\r\n" );
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document.write( "(ii)   Only defect A:        P(A_only) = P(A) - P(A and B) = P(A) - P(A)*P(B) = 0.167 - 0.020875 = 0.146125.\r\n" );
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document.write( "(iiI)  Only defect B:        P(B_only) = P(B) - P(A and B) = P(B) - P(A)*P(B) = 0.125 - 0.020875 = 0.104125.\r\n" );
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document.write( "(iv)   One defect only:      P(A_only) + P(B_only) = the sum from (ii) and (iii) = 0.146125 + 0.104125 = 0.25025.\r\n" );
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document.write( "(v)    At least one defect:  P(A or B) = P(A) + P(B) - P(A and B) = 0.167 + 0.125 - 0.020875 = 0.271125\r\n" );
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