Question

Every cereal box has a gift inside, but you cannot tell them from the outside with the gift is. The store manager assures you that 17 of the 43 boxes on the shelf have the secret decoder ring. The other 26 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 give answer as a decimal correct to at least three decimal places.

Answer 1

P(both of them have the secret decoder ring) = Number of ways in which two cereal boxes with secret decoder rings can be selected from 17 / Number of ways of selecting 2 cereal boxes from 43

= 17C2 / 43C2

= 136/903

= 0.1506

OR

P(both of them have the secret decoder ring) = P(first one has secret decoder ring) x P(second one has secret decoder ring)

= 17/43 x 16/42

= 0.1506