Question

an animal shelter is about to hold an adoption day. the following table represents the number of dogs in each breed that the shelter has at the beginning of the event. assume that no new dogs are brought in on adoption day. what is the probability that the shelters first customer will adopt a beagle, and then the second customer will adopt a golden retriever? enter your answer as either a simplified fraction or a decimal rounded to the nearest hundredth.

dog breed	number
golden retriever	7
malamute	4
chihuahua	2

Explanation:

Step1: Calculate total number of dogs

$6 + 7+4 + 2=19$

Step2: Calculate probability of first - customer adopting a beagle

The probability $P_1$ that the first customer adopts a beagle is the number of beagles divided by the total number of dogs. So $P_1=\frac{6}{19}$.

Step3: Calculate probability of second - customer adopting a golden retriever

After the first customer adopts a beagle, there are $19 - 1=18$ dogs left. The probability $P_2$ that the second customer adopts a golden retriever is the number of golden retrievers divided by the remaining number of dogs. So $P_2=\frac{7}{18}$.

Step4: Calculate the combined probability

Since these are independent - like sequential events, the probability that the first customer adopts a beagle and the second customer adopts a golden retriever is $P = P_1\times P_2$. So $P=\frac{6}{19}\times\frac{7}{18}=\frac{42}{342}=\frac{7}{57}\approx0.12$

Answer:

$\frac{7}{57}\approx0.12$