document.write( "Question 1142322: A company that makes corn flex is putting prize coupons in some of the boxes to as a promotional
\n" ); document.write( "strategy. On a certain day, a Supermarket has nine boxes of this product on its shelves and two of
\n" ); document.write( "these nine boxes contain prize coupons. Suppose that the customer who buys a box picks it from the
\n" ); document.write( "shelf at random. The store sells six of these nine boxes on that day. Find out the following
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\n" ); document.write( "a. None of the six boxes sold contains a prize coupon.
\n" ); document.write( "b. At least one of the six boxes sold contains a prize coupon.
\n" ); document.write( "c. Both of the boxes with prizes are sold on that day.
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Algebra.Com's Answer #763076 by ikleyn(52812) $\"\"$ $\"About$

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document.write( "Among the total 9 boxes, you have 2 boxes with prizes and 9-2 = 7 regular boxes without prizes.\r\n" );
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document.write( "(a)  In this case, the buyers actually selected 6 regular boxes from the set of 7 regular boxes.\r\n" );
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document.write( "     They can do it in  = 7 ways.\r\n" );
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document.write( "     This set is the set of favorable events in this case.\r\n" );
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document.write( "     The total space of events has   =  = 84 elements.\r\n" );
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document.write( "     Therefore, the probability in this case is   = .   ANSWER\r\n" );
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document.write( "(b)  This probability is the complement to the probability of case (a):\r\n" );
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document.write( "     P = 1 -  = .    ANSWER\r\n" );
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document.write( "(c)  We calculate the number of favorable events in this case as follows:\r\n" );
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document.write( "        - you can choose 2 prize boxes from 3 prize boxes by 3 ways, and\r\n" );
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document.write( "        - you can choose the complementary 6-2 = 4 regular boxes from 9-3 = 6 regular boxes by   =  = 15 ways.\r\n" );
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document.write( "        - so the number of favorable events is 3*15 = 45,\r\n" );
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document.write( "        - while the number of all elements of the event space is   = 84.\r\n" );
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document.write( "     So the probability in this case is   = .   ANSWER\r\n" );
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