In a class of 28 students, 19 have a cat and 6 have a dog. There are 5 students who do not have a cat or a dog. What is the probability that a student who has a cat also has a dog?
2/19
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Well, let's see if we can calculate it! We know that there are 28 students in total, and out of those, 6 have a dog. Now, out of the 28 students, 19 have a cat. But hold on a second, we can't assume that those 19 students are separate from the 6 students who have a dog. It's possible that some of them might have both a cat and a dog. So, unfortunately, without more information, it's hard to determine the exact probability. But hey, maybe the cats and dogs are having a secret meeting and figuring it out themselves!
To find the probability that a student who has a cat also has a dog, we need to first determine the number of students who have both a cat and a dog.
Given that there are 28 students in total, 19 have a cat, and 6 have a dog, we can deduce that the number of students who have neither a cat nor a dog is 5.
Let's calculate the number of students who have both a cat and a dog. To do this, we need to subtract the number of students who have a cat only from the total number of students who have a cat.
The number of students who have a cat only can be calculated by subtracting the number of students who have both a cat and a dog from the total number of students who have a cat.
So, let's break it down:
Total students = 28
Students with a cat = 19
Students with a dog = 6
Students with neither a cat nor a dog = 5
Students with both a cat and a dog = Students with a cat - Students with a cat only
Students with a cat only = Students with a cat - Students with both a cat and a dog
Now, let's calculate the value of each:
Students with both a cat and a dog = 19 - (28 - 5) = 19 - 23 = -4
However, we can't have negative students, so the number of students with both a cat and a dog must be 0.
Therefore, the probability that a student who has a cat also has a dog is 0.
If x have both a cat and a dog, then
19+6-x = 28-5
So, since 19 have a cat, P(cat & dog) = x/19