document.write( "Question 1203376: A and B are two events in a sample space. Given that P(A)=0.4 and P(A or B)=0.7.
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\n" ); document.write( "Find the value of P(B) for which A and B are mutually exclusive.
\n" ); document.write( "Find the value of P(B) for which A and B are independent.\r
\n" ); document.write( "\n" ); document.write( "Please note that I am looking for help in my upcoming exams, if you or anyone is interested please leave a contact email address so I can reach out to you and discuss payment. \n" ); document.write( "
Algebra.Com's Answer #838878 by ikleyn(52798)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "A and B are two events in a sample space. Given that P(A)=0.4 and P(A or B)=0.7.
\n" ); document.write( "(a) Find the probability that neither A nor B occurs.
\n" ); document.write( "(b) Find the value of P(B) for which A and B are mutually exclusive.
\n" ); document.write( "(c) Find the value of P(B) for which A and B are independent.
\n" ); document.write( "Please note that I am looking for help in my upcoming exams,
\n" ); document.write( "if you or anyone is interested please leave a contact email address so I can reach out to you and discuss payment.
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document.write( "(a)  The probability that neither A nor B occurs is the COMPLEMENT\r\n" );
document.write( "     to the probability P(A or B).  \r\n" );
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document.write( "     For P(A or B), it is given:  P(A or B) = 0.7.\r\n" );
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document.write( "     THEREFORE, P(neither A nor B) = 1 - P(A or B) = 1 - 0.7 = 0.3.    It is the ANSWER to question (a).\r\n" );
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document.write( "(b)  If A and B are mutually exclusive, it means that they are disjoint. i.e. P(A and B) = 0.\r\n" );
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document.write( "     It implies that P(A or B) = P(A) + P(B), \r\n" );
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document.write( "     and, substituting the given data, we have  0.7 = 0.4 + P(B),\r\n" );
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document.write( "     which implies  P(B) = 0.7 - 0.4 = 0.3.            It is the ANSWER to question (b).\r\n" );
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document.write( "(c)  A and B are independent (by the definition) if and only if P(A and B) = P(A)*P(B).\r\n" );
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document.write( "     Next, we use the general formula  P(A or B) = P(A) + P(B) - P(A and B)\r\n" );
document.write( "     and substitute there  P(A and B) = P(A)*P(B).  It gives us\r\n" );
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document.write( "         P(A or B) = P(A) + P(B) - P(A)*P(B).\r\n" );
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document.write( "     Substitute here the given values. You will get\r\n" );
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document.write( "         0.7 = 0.4 + P(B) - 0.4*P(B).\r\n" );
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document.write( "      Simplify and get P(B)\r\n" );
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document.write( "         0.7 - 0.4 = P(B) - 0.4*P(B)\r\n" );
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document.write( "            0.3    =    0.6*P(B)\r\n" );
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document.write( "            P(B) = \"0.3%2F0.6\" = \"1%2F2\" = 0.5.    It is the ANSWER to question (c).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Below is the listing of relevant formulas on probability that I used in my solution
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document.write( "(1)  General formula of probability P(A or B) = P(A) + P(B) - P(A and B),\r\n" );
document.write( "     which is valid ALWAYS for any events A and B.\r\n" );
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document.write( "(2)  Formula for independent events A and B  P(A and B) = P(A)*P(B).\r\n" );
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document.write( "(3)  Definition of mutually exclusive(= disjoint) events  P(A and B) = 0.\r\n" );
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document.write( "     Formula for probability of mutually exclusive (= disjoint) events   \r\n" );
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document.write( "         P(A or B) = P(A) + P(B).\r\n" );
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document.write( "(4)  Formula for P(neither A nor B)\r\n" );
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document.write( "         P(neither A nor B) = 1 - P(A or B).\r\n" );
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document.write( "(5)  General formula for probability P(nor A) = 1 - P(A)  \r\n" );
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document.write( "     (so called complementary probability).\r\n" );
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\n" ); document.write( "\n" ); document.write( "        Find these formulas and conceptions
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on Elementary Probability theory see these links\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest probability problems \r
\n" ); document.write( "\n" ); document.write( "    - Solving probability problems using complementary probability \r
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\n" ); document.write( "\n" ); document.write( "Try to solve as many of these problems as you can - - - ON  YOUR  OWN.
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook,  handbook,  guidebook,  tutorials
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