Question

in a recent harris poll, a random sample of adult americans (18 years and older) was asked, when you see an ad emphasizing that a product is made in america, are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it? a subset of the results of the survey, by age group, are presented in the accompanying contingency table. using the results of the survey, complete parts (a) through (c)

(a) what is the probability that a randomly selected individual is 35 to 44 years of age, given the individual is neither more nor less likely to buy a product emphasized as made in america?

the probability is approximately
(round to three decimal places as needed.)

Explanation:

Step1: Identify the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of a contingency table, if \(A\) is the event "35 - 44 years of age" and \(B\) is the event "neither more nor less likely", then \(P(A|B)=\frac{\text{Number of people who are 35 - 44 and neither more nor less likely}}{\text{Total number of people who are neither more nor less likely}}\).

Step2: Extract values from the table

From the table, the number of people who are 35 - 44 and neither more nor less likely is \(n(A\cap B) = 201\). The total number of people who are neither more nor less likely is \(n(B)=761\).

Step3: Calculate the probability

Substitute the values into the formula: \(P(A|B)=\frac{201}{761}\approx0.264\).

Answer:

\(0.264\)