Final answer:
The probability that a randomly chosen student has both a cat and a dog is found by using the principle of inclusion-exclusion, resulting in 9 out of 25 students, or a probability of 0.36. This correct probability does not match any of the provided answer choices, indicating a possible error in the question.
Step-by-step explanation:
The student's question is about calculating the probability that a randomly chosen student in a class of 25 students has both a cat and a dog. To find this, first determine the total number of students who have either a cat or a dog or both. We know that 15 students have a cat, 16 have a dog, and 3 have neither. So the total number of students who have a pet is 25 - 3 = 22 students. According to the principle of inclusion-exclusion, the number of students who have both a cat and a dog can be found by adding the number of students who have a cat to the number of students who have a dog and then subtracting the total number of students with a pet.
The calculation is as follows:
Number of students with both a cat and a dog = (Number of students with a cat) + (Number of students with a dog) - (Total number of students with a pet).
So, the number of students with both pets is 15 + 16 - 22 = 9.
Finally, the probability that a randomly chosen student has both a cat and a dog is the number of students with both divided by the total number of students, which is 9/25.
The correct answer is not explicitly listed among the options provided (A) 0.48, (B) 0.60, (C) 0.15, (D) 0.85. However, we can calculate that the probability is 9/25 = 0.36, which is not reflected in the provided choices. There may be an error in the question or in the provided answer choices.