Use the probability distribution to find probabilities in pa

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.)

Solution

(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