In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student chosen randomly from the class does not have a dog?Has a cat Does not have a catHas a dog 10 3Does not have a dog 4 5
Question
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student chosen randomly from the class does not have a dog?Has a cat Does not have a catHas a dog 10 3Does not have a dog 4 5
Solution
To calculate the probability that a student chosen randomly from the class does not have a dog, we first need to find the total number of students and the number of students who do not have a dog.
From the data table, we can see that:
- 10 students have a cat and a dog
- 3 students have a dog but do not have a cat
- 4 students do not have a dog but have a cat
- 5 students do not have a dog or a cat
So, the total number of students in the class is 10 + 3 + 4 + 5 = 22 students.
The number of students who do not have a dog is 4 (those who have a cat but not a dog) + 5 (those who do not have a cat or a dog) = 9 students.
The probability that a student chosen randomly from the class does not have a dog is therefore 9 (students who do not have a dog) divided by 22 (total students), which is approximately 0.409 or 40.9% when expressed as a percentage.
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