In a certian city, 50% of households own a dog, 70% own a cat and 35% own a dog
ID: 3230166 • Letter: I
Question
In a certian city, 50% of households own a dog, 70% own a cat and 35% own a dog and cat. If we select a home at random:
a) What is the probability they own a dog or a cat?
b) What is the probability they do not own a cat?
c) If we know that the household owns a cat, what is the probability that they also own a dog?
d) Is the event "owning a dog" independent of the event of "owning a cat"? Breifly explain.
e) If we select 5 houses at random, and we assume that our selections are independent of one another. What is the probability that we select 2 households that own a cat?
Explanation / Answer
P(dog) = 0.5
P(cat) = 0.7
P(both dog and cat) = 0.35
a) P(dog or cat) = P(dog) + P(cat) - P(dog and cat)
= 0.5 + 0.7 - 0.35
= 0.85
b) P(not owning a cat) = 1 - P(cat) = 1 - 0.35 = 0.65
c) P(dog | cat) = P(dog and cat) / P(cat)
= 0.35 / 0.7
= 0.5
d) Yes, the event "owning a dog" is independent of the event of "owning a cat". Because, P(owning a dog | owning a cat) is equal to P(owning a dog).
e) P(cat) = 0.7
n = 5
P(X = x) = 5Cx * 0.7x * (1 - 0.7)5-x
P(X = 2) = 5C2 * 0.72 * 0.33 = 0.1323