document.write( "Question 1148078: Let A and B be events with P(A)=0.7 and P(B)=0.4, and P( A or B)= 0.8. \r
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\n" ); document.write( "\n" ); document.write( "(b) Are A and B mutually exclusive? Explain\r
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Algebra.Com's Answer #769458 by ikleyn(52887) $\"\"$ $\"About$

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document.write( "(a)  Use the general formula of the Probability theory\r\n" );
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document.write( "         P(A or B) = P(A) + P(B) - P(A and B).\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( "         0.8 = 0.7 + 0.4 - P(A and B) \r\n" );
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document.write( "     From this equation, find  \r\n" );
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document.write( "         P(A and B) = 0.7 + 0.4 - 0.8 = 0.3.\r\n" );
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document.write( "     It is the ANSWER  to question (a).\r\n" );
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document.write( "(b)  Since P(A and B) is not equal to 0 (zero, ZERO),  the events A and B  are NOR mutually exclusive.    ANSWER\r\n" );
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document.write( "     Notice :  for mutually exclusive events X and Y,  P(X and Y) = 0.\r\n" );
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document.write( "(c)  The events X and Y are called independent if  P(X and Y) = P(X)*P(Y).\r\n" );
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document.write( "     Let's check if it is true in our case.\r\n" );
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document.write( "     In (a), we found that  P(A and B) = 0.3.\r\n" );
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document.write( "     From the other side,  P(A)*P(B) = 0.7*0.4 = 0.28.\r\n" );
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document.write( "     Since 0.3 is not equal to 0.28, the events A and B are NOT independent.    ANSWER\r\n" );
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