Use the probability distribution to find probabilities in parts (a) through (c).
ID: 3004305 • Letter: U
Question
Use the probability distribution to find probabilities in parts (a) through (c).
The probability distribution of number of dogs per household in a small town
Dogs 0 1 2 3 4 5
Households 0.680 0.191 0.079 0.029 0.0130 0. 008
(a) Find the probability of randomly selecting a household that has fewer than two dogs.
0.871(Round to three decimal places as needed.)
(b) Find the probability of randomly selecting a household that has at least one dog.
0.320 (Round to three decimal places as needed.)
(c) Find the probability of randomly selecting a household that has between one and three dogs, inclusive.
0.299 (Round to three decimal places as needed.)
Explanation / Answer
(a) Probability of randomly selecting a household that has fewer than two dogs
Probability that household has < 2 dogs = probability of 0 dogs + probability of 1 dog
= 0.680 + 0.191
= 0.871
Probability of randomly selecting a household that has fewer than two dogs = 0.871
(b) Probability of randomly selecting a household that has at least one dog
Probability that household has at least 1 dog = probability that household has > 0 dogs
We know the probability that a household has 0 dogs. So the probability that a household has MORE than 0 dogs means the same as "all possibilities except 0 dogs".
("The probability that x is false = 1 - the probability that x is true". This is called a complement.)
That is = 1 - 0.680
= 0.320
Probability of randomly selecting a household that has at least one dog = 0.320
(c) Probability of randomly selecting a household that has between one and three dogs, inclusive
Probability of 1-3 dogs, inclusive = probability of 1 dog + probability of 2 dogs + probability of 3 dogs
= 0.191 + 0.079 + 0.029
= 0.299
Probability of randomly selecting a household that has between one and three dogs, inclusive = 0.299
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