Answer to Question #347008 in Statistics and Probability for jk1

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 19 of the 49 boxes on the shelf have the secret decoder ring. The other 30 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

The probability to get the secret decoder ring the first time is equals $\frac{19}{49}$ .

The probability of getting the secret decoder ring in the second box is $\frac{18}{48}.$

The probability that BOTH of boxes have the secret decoder ring is

$\frac{19}{49} \cdot \frac{18}{48}=\frac{342}{2352} \approx 0.1454=14.54 \%.$

Answer: $14.54 \%.$