Question

week 6 homework score: 8/22 answered: 8/22 question 9 inside the box of every cereal box contains a surprise gift. the store manager assures employees that 19 of the 50 boxes on the shelf have a secret decoder ring and inside the other 31 boxes on the shelf contain a different gift. if two cereal boxes are randomly selected 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 least three decimal places.)

Explanation:

Step1: Calculate first - pick probability

The probability of picking a box with a secret decoder ring on the first pick is $\frac{19}{50}$ since there are 19 boxes with the secret decoder ring out of 50 total boxes.

Step2: Calculate second - pick probability

After the first box with a secret decoder ring is picked, there are 18 boxes with a secret decoder ring left and 49 total boxes left. So the probability of picking a box with a secret decoder ring on the second pick is $\frac{18}{49}$.

Step3: Calculate joint - probability

The probability that both events occur (both boxes have secret decoder rings) is the product of the probabilities of each event. So $P=\frac{19}{50}\times\frac{18}{49}=\frac{342}{2450}\approx 0.140$.

Answer:

$0.140$