Question

n a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).

Purchase likelihood	18 dash 3418-34	35 dash 4435-44	45 dash 5445-54	55 plus55+	Total
More likelyMore likely	227227	358358	371371	400400	13561356
Less likelyLess likely	2929	66	2222	1212	6969
Neither more nor less likelyNeither more nor less likely	281281	203203	167167	112112	763763
Total	537537	567567	560560	524524	21882188

(a) What is the probability that a randomly selected individual is

35 to 4435 to 44

years of age, given the individual is

more likelymore likely

to buy a product emphasized as "Made in our country"?The probability is approximately

nothing.

(Round to three decimal places as needed.)

Answer 1

Solution:

Given:

Numbers given in tables are repeated in each cell. So I have reconstructed table as below:

"When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?"

Purchase likelihood	18-34	35-44	45-54	55+	Total
More likely	227	358	371	400	1356
Less likely	29	6	22	12	69
Neither more nor less likely	281	203	167	112	763
Total	537	567	560	524	2188

Part a) Find the probability that a randomly selected individual is 35 to 44 years of age, given the individual is more likely to buy a product emphasized as "Made in our country".

Let A : individual is 35 to 44 years of age and

B : the individual is more likely to buy a product emphasized as "Made in our country"

So we have to find : P( A given B) =........?

That is:

P(A | B) = ............?

We use conditional probability formula to find above probability:

where

P(A and B) = Number of individual is 35 to 44 years of age as well as is more likely to buy a product / N

P(A and B) = 358 / 2188

and

P(B) =Number of individual is more likely to buy a product emphasized as "Made in our country" / N

P(B) = 1356 / 2188

Thus

Thus the probability that a randomly selected individual is 35 to 44 years of age, given the individual is more likely to buy a product emphasized as "Made in our country" is : 0.264