Answer:
The proportion of pet owners who were women is 0.540.
The proportion of non-pet owners who were women is 0.493.
Step-by-step explanation:
The data provided is summarized in the table below.
Pet Owners Non-Pet Owners TOTAL
Men 250 1002 1252
Women 293 975 1268
TOTAL 543 1977 2520
Denote the events as follows:
<em>W</em> = a subject is a women
<em>P</em> = a subject is a pet owner
The probability of an event, say E, is defined as the ration of the favorable outcomes of <em>E</em> to the the total number of outcomes of the experiment.
P (E) = n (E) ÷ N
Here,
n (E) = favorable outcome
N = total number of outcomes
(1)
The conditional probability of an event <em>B</em> given that another events <em>A</em> has already occurred is:
P (B | A) = n (A ∩ B) ÷ n (A)
Compute the probability of a pet owner being a women as follows:
P (W | P) = n (W ∩ P) ÷ n (P)
= 975 ÷ 1977
= 0.5396
≈ 0.540
Thus, the proportion of pet owners who were women is 0.540.
(2)
Compute the probability of a non-pet owner being a women as follows:
P (W | P') = n (W ∩ P') ÷ n (P')
= 293 ÷ 543
= 0.4932
≈ 0.493
Thus, the proportion of non-pet owners who were women is 0.493.
