Among dogs in a certain large city, 66 percent were adopted from an animal shelter. Suppose that two dogs will be independently selected at random.

The probability that BOTH selected dogs will have been adopted from an animal shelter is __________ .

 A. 0.7742
 B. 0.4356
 C. 0.812
 D. 0.2614
 E. 0.3485

We are given that 66% of the dogs in a large city were adopted from an animal shelter, and we are asked to find the probability that both of two randomly selected dogs were adopted from a shelter.

To solve this:

1. The probability that one dog was adopted from a shelter is \( P(\text{adopted}) = 0.66 \).
2. Since the two dogs are selected independently, the probability that both dogs were adopted from a shelter is the product of the individual probabilities:
   \[
   P(\text{both adopted}) = P(\text{adopted}) \times P(\text{adopted}) = 0.66 \times 0.66 = 0.4356
   \]

Thus, the probability that both selected dogs were adopted from an animal shelter is \( 0.4356 \).

The correct answer is:

**B. 0.4356**

Would you like more details on how this was calculated or have any questions?

Here are 5 related questions for further practice:

1. What is the probability that neither of the two selected dogs was adopted from an animal shelter?
2. What is the probability that exactly one of the two selected dogs was adopted from an animal shelter?
3. If three dogs are selected independently, what is the probability that all three were adopted from a shelter?
4. If 80% of cats in the same city were adopted from a shelter, what is the probability that both a randomly selected dog and cat were adopted?
5. How does the assumption of independent selection affect the result?

**Tip:** When dealing with independent events, you multiply the probabilities of each event occurring to find the overall probability.

Among dogs in a certain large city, 66 percent were adopted from an animal shelter. Suppose that two dogs will be independently selected at random. The probability that BOTH selected dogs will have been adopted from an animal shelter is __________ .

 A. 0.7742
 B. 0.4356
 C. 0.812
 D. 0.2614
 E. 0.3485

Learn how to calculate the probability that both of two randomly selected dogs in a large city were adopted from an animal shelter. This problem involves key probability concepts, such as independent events and the multiplication rule, and is suitable for high school students (Grades 9-12).

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