SOLUTION: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 13 of the 45 boxes on the shelf have the secret decode
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-> SOLUTION: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 13 of the 45 boxes on the shelf have the secret decode
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Question 1144655: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 13 of the 45 boxes on the shelf have the secret decoder ring. The other 32 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring? Answer by math_helper(2461) (Show Source):
Before choosing any box, there are 13 out of 45 that have the decoder ring, that means your first selection has probability 13/45 of containing a decoder ring.
After the first box has been chosen...
Assuming it had a decoder ring, there are now 12 boxes remaining with decoder rings hidden inside. There are also now only 44 boxes left. Thus the probability of the 2nd box having a decoder ring is 12/44.
The total probability is therefore (13/45)*(12/44) = 156/1980 = (about 0.0788 or 7.88%)
