Question

in 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 - 34 35 - 44 45 - 54 55+ total more likely 225 325 326 403 1279 less likely 23 9 28 17 77 neither more nor less likely 287 209 158 136 790 total 535 543 512 556 2146 (a) what is 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? the probability is approximately 0.254. (round to three decimal places as needed.) (b) what is the probability that a randomly selected individual is more likely to buy a product emphasized as made in our country, given the individual is 35 to 44 years of age? the probability is approximately . (round to three decimal places as needed.)

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the contingency - table, if $A$ is the event of being more likely to buy and $B$ is the event of being 35 - 44 years old, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of people who are 35 - 44 years old and more likely to buy, and $n(B)$ is the number of people who are 35 - 44 years old.

Step2: Identify values from the table

From the table, the number of people who are 35 - 44 years old and more likely to buy $n(A\cap B) = 325$, and the number of people who are 35 - 44 years old $n(B)=543$.

Step3: Calculate the probability

$P=\frac{325}{543}\approx0.599$.

Answer:

$0.599$