Answer:
What is the probability that a randomly selected family owns a cat? 34%
What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat? 82.4%
Step-by-step explanation: We can use a Venn (attached) diagram to describe this situation:
Imagine a community of 100 families (we can assum a number, because in the end, it does not matter)
So, 30% of the families own a dog = .30*100 = 30
20% of the families that own a dog also own a cat = 0.2*30 = 6
34% of all the families own a cat = 0.34*100 = 34
Dogs and cats: 6
Only dogs: 30 - 6 = 24
Only cats: 34 - 6 = 28
Not cat and dogs: 24+6+28 = 58; 100 - 58 = 42
What is the probability that a randomly selected family owns a cat?
34/100 = 34%
What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?
A = doesn't own a dog
B = owns a cat
P(A|B) = P(A∩B)/P(B) = 28/34 = 82.4%
Answer:
the answer is 58.8%
Step-by-step explanation:
From the example given, we apply the use of conditional probability
The general rule for conditional probability is: P(A given B) = Probability of (A and B) / Probability (B).
The Probability of a randomly select family owns a cat is 34%.
The Probability of not owing a dog (A), given that it owns a cat (B) = P(not owing a dog AND owning a cat) / P (owning a cat). which is = x/y so
The relationship between a Cat and Dog is not determined to be independent, thus, we say x just by finding the probability of the two events and multiplying.
Given that 30% own a dog and 20% of those own a cat is 30% x 20% = 6%
7% of all the families own both.
Since 34% own a cat, 34 - 6 = 28% own a cat but not a dog. That gives you x, and y is still just 34%,
So for x/y = 20/34
= 58.8%
