Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 20 of the 63 boxes on the shelf have the secret decoder ring. The other 43 boxes on the shelf have a different gift inside. If randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring? you

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Problem Statement:**

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 20 of the 63 boxes on the shelf have the secret decoder ring. The other 43 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 four decimal places.)*

**Solution Explanation:**

To solve this problem, we need to calculate the probability of drawing two boxes with the secret decoder ring sequentially. 

1. **Total Number of Boxes:** 63.
2. **Boxes with a Secret Decoder Ring:** 20.
3. **Probability of First Box:** The probability that the first box selected has a secret decoder ring is \( \frac{20}{63} \).
4. **Probability of Second Box:** Once the first box has been selected, there are now 62 boxes left in total, with 19 of them having the secret decoder ring. The probability that the second box also has a secret decoder ring is \( \frac{19}{62} \).

**Total Probability:** 

To find the probability that both boxes have the secret decoder ring, multiply the probabilities of each independent event:

\[
P(\text{both boxes have rings}) = \frac{20}{63} \times \frac{19}{62}
\]

Calculate the result and round it to four decimal places.
Transcribed Image Text:**Problem Statement:** Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 20 of the 63 boxes on the shelf have the secret decoder ring. The other 43 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 four decimal places.)* **Solution Explanation:** To solve this problem, we need to calculate the probability of drawing two boxes with the secret decoder ring sequentially. 1. **Total Number of Boxes:** 63. 2. **Boxes with a Secret Decoder Ring:** 20. 3. **Probability of First Box:** The probability that the first box selected has a secret decoder ring is \( \frac{20}{63} \). 4. **Probability of Second Box:** Once the first box has been selected, there are now 62 boxes left in total, with 19 of them having the secret decoder ring. The probability that the second box also has a secret decoder ring is \( \frac{19}{62} \). **Total Probability:** To find the probability that both boxes have the secret decoder ring, multiply the probabilities of each independent event: \[ P(\text{both boxes have rings}) = \frac{20}{63} \times \frac{19}{62} \] Calculate the result and round it to four decimal places.
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