document.write( "Question 626246: Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.
\n" ); document.write( "• G = card drawn is green
\n" ); document.write( "• Y = card drawn is yellow
\n" ); document.write( "• E = card drawn is even-numbered \r
\n" ); document.write( "\n" ); document.write( "List: 1)simple space,
\n" ); document.write( "2)Enter probability P(G) as a fraction
\n" ); document.write( "3)P(G/E)
\n" ); document.write( "4)P(G AND E)
\n" ); document.write( "5)P(G or E)
\n" ); document.write( "6)Are G and E are mutually exclusive
\n" ); document.write( "Thank you so much\r
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Algebra.Com's Answer #394069 by Edwin McCravy(20060) $\"\"$ $\"About$

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Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.
\n" ); document.write( "• G = card drawn is green
\n" ); document.write( "• Y = card drawn is yellow
\n" ); document.write( "• E = card drawn is even-numbered \r
\n" ); document.write( "\n" ); document.write( "List: 1)sample space
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document.write( "{G1,G2,G3,G4,G5,Y1,Y2,Y3}

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\n" ); document.write( "2)Enter probability P(G) as a fraction.

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document.write( "There are 5 G's out of 8 cards, so the probability is \r\n" );
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\n" ); document.write( "3)P(G|E)

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document.write( "We can do this one either of two ways.  Either way gives the same answer.\r\n" );
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document.write( "First way: Reduce the sample space to what is given.  Since we are given\r\n" );
document.write( "E, we reduce the sample space to just those with even numbers, so we\r\n" );
document.write( "delete everything from the sample space in problem 1) that doesn't have\r\n" );
document.write( "an even number, and keep only the ones which do. So the reduced sample \r\n" );
document.write( "space is {G2,G4,Y2}. Now P(G|E) = P(G) using the reduced sample space.  \r\n" );
document.write( "Thats 2 out of 3 or .\r\n" );
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document.write( "Second way: Use the formula for conditional probability:\r\n" );
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document.write( "P(G|E) =  =  =  =  =  =  \r\n" );
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\n" ); document.write( "4)P(G AND E)

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document.write( "There are 2 ways, G2 and G4, to have both Green AND Even out of 8 ways, so\r\n" );
document.write( "the probability P(G AND E) =  =  \r\n" );
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\n" ); document.write( "5)P(G or E)

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document.write( "There are 6 ways, G1,G2,G3,G4,G5 or Y2 to have one OR the other of either \r\n" );
document.write( "Green OR Even. So the probability is  which reduces to .\r\n" );
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document.write( "6)Are G and E are mutually exclusive\r\n" );
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document.write( "Think of the word \"exclusiVE\" as \"excludiNG\". They do not EXCLUDE each other.\r\n" );
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document.write( "They are not mutually exclusive events because to be mutually exclusive events,\r\n" );
document.write( "the two events must be such that if one of them is true the other MUST BE\r\n" );
document.write( "false.  In other words, the truth of one would have to EXCLUDE the other.    \r\n" );
document.write( "Here Green does not EXCLUDE Even, because for instance, we could\r\n" );
document.write( "draw G2.  \r\n" );
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document.write( "Edwin

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