Math

QuestionIn a class, 4 students have both a cat and a dog, 7 have a dog but no cat, 16 have a cat but no dog, and 2 have neither. Find the probability that a randomly chosen student has a cat or a dog.

Studdy Solution

STEP 1

Assumptions1. The number of students who have a cat and a dog is4. . The number of students who have a dog but not a cat is7.
3. The number of students who have a cat but not a dog is16.
4. The number of students who neither have a cat nor a dog is.
5. The student is chosen randomly from the class.

STEP 2

First, we need to find the total number of students in the class. We can do this by adding the number of students in each category.
Totalstudents=Studentswithcatanddog+Studentswithdogbutnocat+Studentswithcatbutnodog+StudentswithneithercatnordogTotal\, students = Students\, with\, cat\, and\, dog + Students\, with\, dog\, but\, no\, cat + Students\, with\, cat\, but\, no\, dog + Students\, with\, neither\, cat\, nor\, dog

STEP 3

Now, plug in the given values for each category to calculate the total number of students.
Totalstudents=+7+16+2Total\, students = +7 +16 +2

STEP 4

Calculate the total number of students in the class.
Totalstudents=4+7+16+2=29Total\, students =4 +7 +16 +2 =29

STEP 5

Next, we need to find the number of students who have either a cat or a dog. We can do this by adding the number of students who have a cat and a dog, the number of students who have a dog but not a cat, and the number of students who have a cat but not a dog.
Studentswithcatordog=Studentswithcatanddog+Studentswithdogbutnocat+StudentswithcatbutnodogStudents\, with\, cat\, or\, dog = Students\, with\, cat\, and\, dog + Students\, with\, dog\, but\, no\, cat + Students\, with\, cat\, but\, no\, dog

STEP 6

Now, plug in the given values for each category to calculate the number of students who have either a cat or a dog.
Studentswithcatordog=4++16Students\, with\, cat\, or\, dog =4 + +16

STEP 7

Calculate the number of students who have either a cat or a dog.
Studentswithcatordog=4+7+16=27Students\, with\, cat\, or\, dog =4 +7 +16 =27

STEP 8

Now that we have the number of students who have either a cat or a dog and the total number of students, we can find the probability that a student chosen randomly from the class has a cat or a dog. The probability is given by the ratio of the number of students who have either a cat or a dog to the total number of students.
Probability=StudentswithcatordogTotalstudentsProbability = \frac{Students\, with\, cat\, or\, dog}{Total\, students}

STEP 9

Plug in the values for the number of students who have either a cat or a dog and the total number of students to calculate the probability.
Probability=2729Probability = \frac{27}{29}The probability that a student chosen randomly from the class has a cat or a dog is 2729\frac{27}{29}.

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