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?
done, look back
To find the probability that both boxes contain the secret decoder ring, you need to determine the probability of selecting a box with the decoder ring for each of the two selections and then multiply these probabilities together.
First, let's find the probability of choosing a box with the secret decoder ring on the first selection. Since there are 16 boxes with the ring out of 58 total boxes, the probability of selecting one of these boxes is 16/58.
Next, after selecting a box with the secret decoder ring on the first selection, there are now only 15 boxes with the ring left out of 57 total boxes. Therefore, for the second selection, the probability of choosing a box with the decoder ring is 15/57.
To find the probability of both events occurring, we multiply the probabilities:
(16/58) * (15/57) = 0.067
So, the probability that BOTH boxes have the secret decoder ring is approximately 0.067, or 6.7%.