document.write( "Question 1210208: A jewelry box contains two gold hoop earrings and two silver hoop earrings. You randomly choose two earrings. What is the probability that both are silver hoop earrings? Write your answer as a simplified fraction. \n" ); document.write( "
Algebra.Com's Answer #851635 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Ikleyn is wrong.  She is thinking that just because we humans cannot tell the\r\n" );
document.write( "difference between two earrings that look identical to us, that they are exactly\r\n" );
document.write( "the same two things.  But they are not.  Put them under a microscope and you\r\n" );
document.write( "will find they are quite different things.  \r\n" );
document.write( "\r\n" );
document.write( "Think of putting a tiny label on each earring, the labels being S1,S2,G1,G2.\r\n" );
document.write( "\r\n" );
document.write( "Would that make it less likely to choose the pair labeled (S1,S2)?  No, it would\r\n" );
document.write( "not!!  But in Ikleyn's way of thinking here it would be.  \r\n" );
document.write( "\r\n" );
document.write( "If she will think about it long and hard she will understand that the\r\n" );
document.write( "probability of getting two silver hoop earrings is exactly the same, 1/6,\r\n" );
document.write( "whether labels were placed on the earrings or not. \r\n" );
document.write( "\r\n" );
document.write( "It should be brought to Ikleyn's and everybody's attention that NO TWO THINGS\r\n" );
document.write( "ARE REALLY AND TRULY INDISTINGUISHABLE!  Not under a microscope!   \r\n" );
document.write( "\r\n" );
document.write( "Even though many math problems state that things are indistinguishable, that\r\n" );
document.write( "only means that they are talking about the way they look to us humans.  But in\r\n" );
document.write( "reality, no two things are exactly alike.  Not exactly!!\r\n" );
document.write( "\r\n" );
document.write( "The word \"indistinguishable\" should only and always be taken to mean\r\n" );
document.write( "\"indistinguishable TO HUMANS' EYES\".\r\n" );
document.write( "\r\n" );
document.write( "In math problems that deal with \"indistinguishable things\", they are always\r\n" );
document.write( "speaking of the number of different ways we humans would consider two things to\r\n" );
document.write( "appear different to our human eyes.  They are not speaking of two things being\r\n" );
document.write( "exactly alike atom by atom, for no two things are exactly alike.  \r\n" );
document.write( "\r\n" );
document.write( "A jewelry box contains two gold hoop earrings and two silver hoop\r\n" );
document.write( "earrings. \r\n" );
document.write( "\r\n" );
document.write( "There are four different things, whether some of them look the same to us humans\r\n" );
document.write( "or not.\r\n" );
document.write( " \r\n" );
document.write( "1.  S1, silver hoop earring #1\r\n" );
document.write( "2.  S2, silver hoop earring #2 \r\n" );
document.write( "3.  G1, gold hoop earring #1\r\n" );
document.write( "4.  G2, gold hoop earring #2\r\n" );
document.write( "\r\n" );
document.write( "You randomly choose two earrings.  \r\n" );
document.write( "\r\n" );
document.write( "The possible choices are\r\n" );
document.write( "\r\n" );
document.write( "1. S1 and S2  <-- the only choice that they are both silver hoop earrings\r\n" );
document.write( "2. S1 and G1\r\n" );
document.write( "3. S1 and G2\r\n" );
document.write( "4. S2 and G1\r\n" );
document.write( "5. S2 and G2\r\n" );
document.write( "6. G1 and G2\r\n" );
document.write( "\r\n" );
document.write( "What is the probability that both are silver hoop earrings?  \r\n" );
document.write( "\r\n" );
document.write( "The only choice that contains both silver hoop earrings is choice 1 above.\r\n" );
document.write( "\r\n" );
document.write( "That's 1 choice out of 6.\r\n" );
document.write( "\r\n" );
document.write( "Write your answer as a simplified fraction.\r\n" );
document.write( "\r\n" );
document.write( "The probability is 1/6.  \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );