In a class of students, the following data table summarizes how many students have a cat or a dogWhat is the probability that a student has a dog given that they have a cat? Has a cat Does not have a cat Has a dog 92 Does not have a dog 14 5
To find the probability that a student has a dog given that they have a cat, we need to calculate the conditional probability.
Conditional probability can be calculated using the formula:
P(A|B) = P(A and B) / P(B)
In this case, "A" represents having a dog and "B" represents having a cat.
From the table, we can see that the number of students who have a cat and a dog is 92. The total number of students who have a cat is 92 + 5 = 97.
So, P(Dog|Cat) = 92 / 97 ≈ 0.9485
Therefore, the probability that a student has a dog given that they have a cat is approximately 0.9485 or 94.85%.