assignment 4.2 - 4.3 addition & multiplication rule, conditional probability\nscore: 12/23 answered…

assignment 4.2 - 4.3 addition & multiplication rule, conditional probability\nscore: 12/23 answered: 12/23\nquestion 13\nevery cereal box has a gift inside, but you cannot tell from the outside what the gift is. the store manager assures you that 21 of the 59 boxes on the shelf have the secret decoder ring. the other 38 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?\n(give answer as a decimal correct to at least three decimal places.)\nprobability =

assignment 4.2 - 4.3 addition & multiplication rule, conditional probability\nscore: 12/23 answered: 12/23\nquestion 13\nevery cereal box has a gift inside, but you cannot tell from the outside what the gift is. the store manager assures you that 21 of the 59 boxes on the shelf have the secret decoder ring. the other 38 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?\n(give answer as a decimal correct to at least three decimal places.)\nprobability =

Answer

Explanation:

Step1: Identify the probability of the first selection

The total number of boxes is 59, and 21 contain the secret decoder ring. $$P(\text{First box has ring}) = \frac{21}{59}$$

Step2: Identify the probability of the second selection

Since one box with a ring was already taken, 20 rings remain out of 58 total boxes. $$P(\text{Second box has ring} | \text{First box had ring}) = \frac{20}{58}$$

Step3: Apply the multiplication rule for dependent events

Multiply the probabilities of the first and second events to find the joint probability. $$P(\text{Both}) = \frac{21}{59} \times \frac{20}{58}$$

Step4: Calculate the final decimal value

Perform the multiplication and division, rounding to at least three decimal places. $$\frac{420}{3422} \approx 0.122735$$

Answer:

probability = 0.123