document.write( "Question 347965: You have 5 keys on a key ring, 2 of the keys unlock the door. Find the
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Algebra.Com's Answer #248858 by Edwin McCravy(20060)\"\" \"About 
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You have 5 keys on a key ring, 2 of the keys unlock the door. Find the
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document.write( "Answer:  We add the two probabilities of successes\r\n" );
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document.write( "2/5 + 3/10 in red above.\r\n" );
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document.write( "                            2/5 + 3/10 = 4/10 + 3/10 = 7/10\r\n" );
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document.write( "Or we could subtract the probability of two wrong keys 3/10 from 1\r\n" );
document.write( "and get 1 - 3/10 = 7/10.\r\n" );
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document.write( "Explanation:  The upper left branch represents picking a right key\r\n" );
document.write( "the first time with a probability of 2 right keys out of 5, or 2/5.\r\n" );
document.write( "That led to a success (opening the door).  So we write 2/5 on the\r\n" );
document.write( "branch that leads to that, and we do not branch from because we\r\n" );
document.write( "open the door. \r\n" );
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document.write( "The lower left branch represents picking a wrong key the first time \r\n" );
document.write( "with a probability of 3 wrong keys out of 5, or 3/5. So we write\r\n" );
document.write( "3/5 on the lower left branch.  So we must branch again from there.\r\n" );
document.write( "There are two possibilities for the second key we try.  We have\r\n" );
document.write( "eliminated 1 wrong key, so we only have 4 keys to try, 2 are wrong\r\n" );
document.write( "keys, and 2 are right keys.  So it's a probability of 2 right keys \r\n" );
document.write( "out of 4 for picking the right key the second time and also a 2 \r\n" );
document.write( "wrong keys out of 4 for picking the wrong key the second time. That's\r\n" );
document.write( "why I wrote 2/4 instead of reducing it to 1/2.\r\n" );
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document.write( "Edwin
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