document.write( "Question 1158727: 1) 6 cars are picked randomly from a garage which has 4 blacks cars and 2 white cars and 4 red cars find the probability of getting at MOST 1 red car.\r
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Algebra.Com's Answer #852958 by ikleyn(53339) $\"\"$ $\"About$

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\n" ); document.write( "(1) 6 cars are picked randomly from a garage which has 4 blacks cars and 2 white cars and 4 red cars
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\n" ); document.write( "(2) 6 cars are picked randomly from a garage which has 4 black cars and 2 white cars and 4 red cars
\n" ); document.write( "find the probability of getting at LEAST 1 red car
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\n" ); document.write( "\n" ); document.write( " (1) Find the probability of getting at MOST 1 red car\r
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document.write( "The total number of cars in the garage is 4 + 2 + 4 = 10.\r\n" );
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document.write( "The probability under the question is the sum of probabilities to get 0 red cars or to get 1 red car,\r\n" );
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document.write( "     P = P(0) + P(1).\r\n" );
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document.write( "The number of ways to get 0 red cars is 1: it is the case to get 4 black and 2 white cars.\r\n" );
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document.write( "The number of ways to get 1 red car of 6 picked cars is equal to the number to comprise 5 cars from (4+2) = 6 cars\r\n" );
document.write( "of the not-red color, multiplied by 4, which is the number to select 1 red car from 4 red cars.\r\n" );
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document.write( "So, the number of ways to get 1 red car of 6 picked cars is\r\n" );
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document.write( "   C(6,5)*(C4,1) = 6*4 = 24.\r\n" );
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document.write( "The total number to get 6 cars from 10 cars is  C(10,6) = 210.\r\n" );
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document.write( "Therefore, the probability under the question (1) is   =  = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( " (2) Find the probability of getting at LEAST 1 red car\r
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document.write( "The probability of getting at LEAST 1 red car is the COMPLEMENT to the probability to get no one red car.\r\n" );
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document.write( "There is only one way to get no one red car: it is to get 4 black cars and 2 white cars\r\n" );
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document.write( "So, the probability to get no one red car is  P' =  = .    \r\n" );
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document.write( "Thus, the answer to question (2) is  P = 1 - P' = 1 -  = 1 -  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Part (2) is solved, too.\r
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