Question

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 16 of the 58 boxes on the shelf have the secret decoder ring. The other 42 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 1

prob of ring = 16/58

prob(2 rings in 2 draws)
= (16/58)(15/57)
= 40/551

or
C(16,2)/(C(58,2))
= 120/1653
= 40/551

Answer 2

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 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?