document.write( "Question 1197263: three biased coins C1,C2,C3l ie on the table .Their probabilities of falling heads are 1/3,2/3 and1 respectiely . A coin is picked at random, tossed twice ,and observed to fall heads both times .Calculate the probability that it is C1. \n" ); document.write( "

Algebra.Com's Answer #830474 by ikleyn(52833) $\"\"$ $\"About$

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\n" ); document.write( "three biased coins C1, C2, C3 $\"highlight%28cross%28ie%29%29\"$ lie on the table.
\n" ); document.write( "Their probabilities of falling heads are 1/3, 2/3 and 1, respectively.
\n" ); document.write( "A coin is picked at random, tossed twice, and observed to fall heads both times.
\n" ); document.write( "Calculate the probability that it is C1.
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document.write( "They want you calculate the conditional probability that the randomly picked coin is C1 \r\n" );
document.write( "given that tossed twice it produces (Head,Head).\r\n" );
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document.write( "    P(tossing one of the three coins twice gives HH) =  =  = \r\n" );
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document.write( "                                                     =  = .\r\n" );
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document.write( "    P(choosing C1 and (tossing C1 twice gives HH)) =  = .\r\n" );
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document.write( "Therefore, the ANSWER is\r\n" );
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document.write( "    P = P(choosing C1 and (tossing C1 twice gives HH)) / P(tossing one of the three coins twice gives HH) =  =  = .\r\n" );
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