Problem

The following frequency table summarizes how many animals are surrendered to a local animal shelter daily. \begin{tabular}{|c|c|} \hline Dogs & 6 \\ \hline Cats & 9 \\ \hline Rabbits & 4 \\ \hline Birds & 5 \\ \hline \end{tabular} Using experimental probability, what is the probability that a cat will be surrendered tomorrow? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. Answer 2 Points Keyboard Shortcut

Solution

Step 1 :Given the frequency table of animals surrendered to a local animal shelter daily, we have the following data: \(\text{Dogs} = 6\), \(\text{Cats} = 9\), \(\text{Rabbits} = 4\), and \(\text{Birds} = 5\).

Step 2 :The total number of animals surrendered daily is the sum of all these animals. So, \(\text{Total animals} = 6 + 9 + 4 + 5 = 24\).

Step 3 :The experimental probability of an event is calculated by dividing the number of times the event occurs by the total number of trials. In this case, the event is a cat being surrendered and the total number of trials is the total number of animals surrendered.

Step 4 :To find the probability that a cat will be surrendered tomorrow, we need to divide the number of cats surrendered by the total number of animals surrendered. So, \(\text{Probability of a cat being surrendered} = \frac{\text{Number of cats surrendered}}{\text{Total number of animals surrendered}} = \frac{9}{24} = 0.375\).

Step 5 :Final Answer: The probability that a cat will be surrendered tomorrow is \(\boxed{0.375}\).

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