A random sample was taken from Wyoming. Eighty percent of students reported that they like dogs, 64% reported they like cats, and 97% reported that they like dogs or cats. What percentage of students like both dogs and cats?
P(D or C) = P(D)+P(C)-P(D and C)
.97 = .80 + .64 - P(D and C)
P(D and C) = .47
To find the percentage of students who like both dogs and cats, we can use the concept of inclusion-exclusion principle.
First, we know that 97% of students reported that they like dogs or cats. This means that at least 97% of students like either dogs or cats or both.
Second, we know that 80% of students reported that they like dogs. This means that at least 80% of students like dogs.
Third, we know that 64% of students reported that they like cats. This means that at least 64% of students like cats.
Now, let's find the percentage of students who like both dogs and cats. Since the percentage of students who like dogs or cats is 97%, we can subtract the percentage of students who only like dogs or only like cats from this total.
Students who only like dogs = Percentage of students who like dogs - Percentage of students who like both dogs and cats
So, students who only like dogs = 80% - X (percentage who like both dogs and cats)
Similarly, students who only like cats = 64% - X (percentage who like both dogs and cats)
We know that the total percentage of students who like dogs or cats is 97%. Therefore, we can write the equation:
80% - X + 64% - X + X = 97%
Simplifying this equation:
144% - 2X + X = 97%
144% - X = 97%
-X = 97% - 144%
-X = -47%
Solving for X:
X = 47%
Therefore, the percentage of students who like both dogs and cats is 47%.