SOLUTION: A company that makes corn flex is putting prize coupons in some of the boxes to as a promotional strategy. On a certain day, a Supermarket has nine boxes of this product on its s

Question 1142322: A company that makes corn flex is putting prize coupons in some of the boxes to as a promotional
strategy. On a certain day, a Supermarket has nine boxes of this product on its shelves and two of
these nine boxes contain prize coupons. Suppose that the customer who buys a box picks it from the
shelf at random. The store sells six of these nine boxes on that day. Find out the following
probabilities,
a. None of the six boxes sold contains a prize coupon.
b. At least one of the six boxes sold contains a prize coupon.
c. Both of the boxes with prizes are sold on that day.

Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.


Among the total 9 boxes, you have 2 boxes with prizes and 9-2 = 7 regular boxes without prizes.



(a)  In this case, the buyers actually selected 6 regular boxes from the set of 7 regular boxes.


     They can do it in  = 7 ways.

     This set is the set of favorable events in this case.

     The total space of events has   =  = 84 elements.


     Therefore, the probability in this case is   = .   ANSWER




(b)  This probability is the complement to the probability of case (a):


     P = 1 -  = .    ANSWER




(c)  We calculate the number of favorable events in this case as follows:


        - you can choose 2 prize boxes from 3 prize boxes by 3 ways, and

        - you can choose the complementary 6-2 = 4 regular boxes from 9-3 = 6 regular boxes by   =  = 15 ways.

        - so the number of favorable events is 3*15 = 45,

        - while the number of all elements of the event space is   = 84.


     So the probability in this case is   = .   ANSWER

All questions are answered : the problem is solved.

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