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.

(b) Find the probability of randomly selecting a household that has at least one dog.

(Round to three decimal places as needed.)

(c) Find the probability of randomly selecting a household that has between one and three dogs, inclusive.

(a) P (x < 2) = 0.871

(b) P (x ≥ 1) = 0.320

(c) P (1 ≤ x ≤ 3) = 0.299

Step-by-step explanation:

We are given the probability distribution of the number of dogs per household in a small town.

Dogs | Households

0 | 0.680

1 | 0.191

2 | 0.079

3 | 0.029

4 | 0.0130

5 | 0.008

(a) Find the probability of randomly selecting a household that has fewer than two dogs.

Fewer than two dogs mean having 0 dog or 1 dog so

P (x < 2) = P (x = 0) + P (x = 1)

P (x < 2) = 0.680 + 0.191

P (x < 2) = 0.871

(b) Find the probability of randomly selecting a household that has at least one dog.

at least one dog means one or greater than one so

P (x ≥ 1) = P (x = 1) + P (x = 2) + P (x = 3) + P (x = 4) + P (x = 5)

P (x ≥ 1) = 0.191 + 0.079 + 0.029 + 0.0130 + 0.008

P (x ≥ 1) = 0.320

Alternatively:

P (x ≥ 1) = 1 - P (x < 1)

P (x ≥ 1) = 1 - P (x = 0)

P (x ≥ 1) = 1 - 0.680

P (x ≥ 1) = 0.320

(c) Find the probability of randomly selecting a household that has between one and three dogs, inclusive.

P (1 ≤ x ≤ 3) = P (x = 1) + P (x = 2) + P (x = 3)

P (1 ≤ x ≤ 3) = 0.191 + 0.079 + 0.029

P (1 ≤ x ≤ 3) = 0.299