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3 of 53 of 5 Items Question In a class of 24 students, 5 have a cat and 13 have a dog. There are 9 students who do not have a cat or a dog. What is the probability that a student chosen randomly from the class does not have a cat? Type your answer as a fraction OR a decimal rounded to 3 decimal places(1 point) The probabilty that a student does NOT have a cat is: Skip to navigation

1 answer

To find the probability that a randomly chosen student does not have a cat, we first need to determine how many students do not have a cat.

  1. Total Students: 24
  2. Students with a Cat: 5
  3. Students without a Cat: \( 24 - 5 = 19 \)

Now, the probability that a student chosen randomly does not have a cat is given by the formula:

\[ P(\text{not having a cat}) = \frac{\text{Number of students without a cat}}{\text{Total number of students}} \]

Substituting the values:

\[ P(\text{not having a cat}) = \frac{19}{24} \]

To express this as a decimal, we can perform the division:

\[ 19 \div 24 \approx 0.79167 \]

Rounding this to three decimal places gives:

\[ P(\text{not having a cat}) \approx 0.792 \]

So, the final answer is:

Probability that a student does NOT have a cat: \(\frac{19}{24}\) or 0.792