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 has a dog given that they do not have a cat?Has a cat Does not have a catHas a dog 3 10Does not have a dog 6 2
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 has a dog given that they do not have a cat?Has a cat Does not have a catHas a dog 3 10Does not have a dog 6 2
Solution
To find the probability that a student has a dog given that they do not have a cat, we need to focus on the column "Does not have a cat" in the table.
Step 1: Identify the total number of students who do not have a cat. This is the sum of the students who have a dog and do not have a cat (10) and the students who do not have a dog and do not have a cat (2). So, the total number of students who do not have a cat is 10 + 2 = 12.
Step 2: Identify the number of students who have a dog and do not have a cat. From the table, this is 10.
Step 3: The probability that a student has a dog given that they do not have a cat is the number of students who have a dog and do not have a cat divided by the total number of students who do not have a cat. So, the probability is 10 / 12 = 0.833 or 83.3%.
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