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 1142618: 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 greenestamps(13200) (Show Source): You can put this solution on YOUR website!

a. P(none of the 6 boxes contains a prize coupon)

6 of the 9 boxes are sold: 6 of the 7 boxes with no prize coupon and 0 of the 2 boxes with a prize coupon:

Alternative method....

P(1st box does not contain a prize coupon) = 7/9
P(2nd box does not contain a prize coupon) = 6/8
P(3rd box does not contain a prize coupon) = 5/7
...
P(6th box does not contain a prize coupon) = 2/4

P(none of the 6 contain a prize coupon) = (7/9)(6/8)(5/7)...(2/4)

You should of course get the same answer by both methods.

b. P(at least one of the 6 boxes contains a prize coupon)

"At least one" means "NOT none of them"; so 1 minus the answer from part a.

c. P(both of the boxes with prize coupons are sold)

6 of the 9 boxes are sold: 4 of the 7 boxes without a prize coupon and both of the 2 with a prize coupon:

As with many fairly basic probability problems, it is a good idea to calculate the probabilities for all possible outcomes as a check of your calculations. If the sum of the probabilities is not 1, your answers are not right.

P(1 of the 2 boxes with a prize coupon is sold)

RELATED QUESTIONS
A company that makes corn flex is putting prize coupons in some of the boxes to as a... (answered by ikleyn)

A company that makes crayons is trying to decide which 5 colors to include in a... (answered by FrankieVlad)

I APPRECIATE ANY HELP AT ALL!!! I just don't know what to do to start with... Each... (answered by ewatrrr,ScientificArt)

Of 350 male and 280 female employees at the home office of Gibraltar Insurance Company,... (answered by ikleyn)

Suppose that you're in desperate need of some cash, and a local restaurant owner offers... (answered by ikleyn)

A chocolate company randomly fills boxes of 10 pieces of chocolate with differently typed (answered by stanbon)

A large fast-food restaurant is having a promotional game where game pieces can be found... (answered by ikleyn)

A certain electronics company produces a particular type of vacuum tube. It has been... (answered by ewatrrr)

The question was According to USA today, only 3.2% of all product coupons are redeemed.... (answered by stanbon)