In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 27% of all the families own a cat.What is the probability that a randomly selected family owns both a dog and a cat?What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

Answer:a) 0.06b) 0.778Step-by-step explanation:Let's suppose a community of 100 families just to facilitate the calculation.30% of the families own a dogDog = 30% of 100 = 3020% of the families that own a dog also own a cat = 20% of 30 = 627% of all the families own a cat = 27% of 100 = 27So, 6 families own a dog and a cat.As 30 families own a dog, [30 - 6 =] 24 families own only dogsAs 27 families own a cat, [27 - 6 = ] 21 families own only catsSee picture attached.a) What is the probability that a randomly selected family owns both a dog and a cat?P(dog and cat) = dog ∩ cat/total = 6/100 = 0.06b) What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?So, only cat/total catP (not dog|cat) = 21/27 = 0.778