document.write( "Question 1154150: We select three balls randomly (one after another) of a box contains 1 white, 2 yellow and 3 blue balls. If all balls have the same chance of selecting, then:
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Algebra.Com's Answer #776559 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "With this kind of problem, you must specify whether it's \"SELECTING WITH\r\n" );
document.write( "REPLACEMENT\" or \"SELECTING WITHOUT REPLACEMENT\".  You didn't specify I will have\r\n" );
document.write( "to do it both ways.\r\n" );
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document.write( "If it's WITHOUT replacing, then we will think of reaching in one time and\r\n" );
document.write( "drawing out 3, so we will use combinations, for you don't care which of the\r\n" );
document.write( "three balls is drawn first, second or third when you just reach in and get a\r\n" );
document.write( "handful of 3 balls.  \r\n" );
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document.write( "a) What is the probability that the selected balls have the same color?\r\n" );
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document.write( "WITHOUT REPLACEMENT:\r\n" );
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document.write( "There is only 1 'successful' way, which is to choose all 3 blue balls.\r\n" );
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document.write( "The number of ways to choose ANY three balls is  \r\n" );
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document.write( "6 balls CHOOSE 3 = 6C3 = 20\r\n" );
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document.write( "So the probability is 1 way out of 20 or 1/20 or 0.05 or 5% of the time.\r\n" );
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document.write( "a) What is the probability that the selected balls have the same color ?\r\n" );
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document.write( "WITH REPLACEMENT:\r\n" );
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document.write( "Case 1: three whites.\r\n" );
document.write( "The first drawn is white, we do that 1/6 of the time.\r\n" );
document.write( "The second drawn is white, we also do that 1/6 of the time.\r\n" );
document.write( "The third drawn is white, we also do that 1/6 of the time.\r\n" );
document.write( "So (1/6)³ = 1/216 of the time we'll draw 3 whites.\r\n" );
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document.write( "Case 2: three yellows.\r\n" );
document.write( "The first drawn is yellow, we do that 2/6 or 1/3 of the time.\r\n" );
document.write( "The second drawn is yellow, we also do that 2/6 or 1/3 of the time.\r\n" );
document.write( "The third drawn is yellow, we also do that 2/6 or 1/3 of the time.\r\n" );
document.write( "So (1/3)³ = 1/27 of the time we'll draw 3 yellows.\r\n" );
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document.write( "Case 3: three blues.\r\n" );
document.write( "The first drawn is blue, we do that 3/6 or 1/2 of the time.\r\n" );
document.write( "The second drawn is blue, we do that 3/6 or 1/2 of the time.\r\n" );
document.write( "The third drawn is blue, we do that 3/6 or 1/2 of the time.\r\n" );
document.write( "So (1/2)³ = 1/8 of the time we'll draw 3 blues.\r\n" );
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document.write( "So the total probability for all three cases is\r\n" );
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document.write( "b) What is the probability that no white balls have been selected?\r\n" );
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document.write( "WITHOUT REPLACING:\r\n" );
document.write( "That means we draw 3 balls from the 5 non-white balls. \r\n" );
document.write( "That's 5 non-white balls CHOOSE 3 or 5C3 = 10 ways.\r\n" );
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document.write( "10 ways out of 20 is 10/20 with reduces to 1/2 \r\n" );
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document.write( "WITH REPLACING.\r\n" );
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document.write( "c) What is the probability that all [BOTH] yellow balls are selected ?\r\n" );
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document.write( "We pick the two yellows 1 way.\r\n" );
document.write( "We pick the 1 non-yellow to go with the two yellows in 4 ways.\r\n" );
document.write( "So there are 1∙4=4 ways to have a combination of 3 including both yellows.\r\n" );
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document.write( "That's 4 ways out of 20 or 4/20 which reduces to 1/5.\r\n" );
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document.write( "Edwin
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