SOLUTION: in a large city, the proportion of households having a dog is 0.4.The proportion of households having a cat is 0.3. The proportion of households having both a dog and a cat is 0.15

Algebra ->  Probability-and-statistics -> SOLUTION: in a large city, the proportion of households having a dog is 0.4.The proportion of households having a cat is 0.3. The proportion of households having both a dog and a cat is 0.15      Log On


   

Question 1137226: in a large city, the proportion of households having a dog is 0.4.The proportion of households having a cat is 0.3. The proportion of households having both a dog and a cat is 0.15. What is the proportion of households has neither a dog nor a cat?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Define two events
A = owning a dog
B = owning a cat

Given info:
P(A) = 0.4
P(B) = 0.3
P(A and B) = 0.15

Use the given info to compute the probability of selecting a household that has either pet
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.4 + 0.3 - 0.15
P(A or B) = 0.7 - 0.15
P(A or B) = 0.55
The probability of having either a cat, a dog, or both is 0.55

Subtract that result from 1 to find the probability of having neither pet
P(not A and not B) = 1 - P(A or B)
P(not A and not B) = 1 - 0.55
P(not A and not B) = 0.45
so 45% of the population of households has neither pet

Answer: 0.45