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Eloise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of soup, and 1 can of peaches. Her son Andy, takes the labels off the cans and throws them away. Eloise then chooses 2 cans at random to open. Find the probability that she will open at least 1 can of soup. \r
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document.write( "Whenever you see the words \"at least one\" \r\n" );
document.write( "always think of this principle:\r\n" );
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document.write( "P(at least one) = 1 - P(none at all)\r\n" );
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document.write( "So therefore\r\n" );
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document.write( "P(she will open at least 1 can of soup) =\r\n" );
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document.write( "1 - P(she will open no cans of soup) =\r\n" );
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document.write( "1 - P(she will open 2 of the 3 non-soup cans) =\r\n" );
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document.write( " no. of ways to choose 2 of the 3 non-soup cans\r\n" );
document.write( "1 - --------------------------------------------------\r\n" );
document.write( " no. of ways to choose any 2 of the 5 cans\r\n" );
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document.write( " C(3,2) 3 7\r\n" );
document.write( "1 - ------- = 1 - ---- = ---- = 0.7\r\n" );
document.write( " C(5,2) 10 10\r\n" );
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document.write( "It's not too hard to check this:\r\n" );
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document.write( "Suppose the 2 cans of vegetables are called V1 and V2 \r\n" );
document.write( "Suppose the 2 cans of soup are called S1 and S2\r\n" );
document.write( "Suppose the 1 can of peaches is called P.\r\n" );
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document.write( "So she can choose any of these ten pairs of cans:\r\n" );
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document.write( " 1. {V1,V2} \r\n" );
document.write( " 2. {V1,S1} at least one soup can \r\n" );
document.write( " 3. {V1,S2} at least one soup can \r\n" );
document.write( " 4. {V1,P}\r\n" );
document.write( " 5. {V2,S1} at least one soup can\r\n" );
document.write( " 6. {V2,S2} at least one soup can \r\n" );
document.write( " 7. {V2,P}\r\n" );
document.write( " 8. {S1,S2} at least one soup can\r\n" );
document.write( " 9. {S1,P} at least one soup can\r\n" );
document.write( "10. {S2,P} at least one soup can\r\n" );
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document.write( "She will have at least one can of soup if\r\n" );
document.write( "she chooses 2, 3, 5, 6, 7, 9, or 10. That's\r\n" );
document.write( "7 out of 10, or a probability of 7/10.\r\n" );
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document.write( "Edwin \n" );
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