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 0.264
(round to three decimal places as needed.)

(b) what is the probability that a randomly selected individual is neither more nor less likely to buy a product emphasized as \made in america,\ given the individual is 35 to 44 years of age?
the probability is approximately
(round to three decimal places as needed.)

Explanation:

Step1: Recall 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 "neither more nor less likely" and \(B\) is the event "35 - 44 years of age", then \(P(A|B)=\frac{\text{Number of people in }A\cap B}{\text{Number of people in }B}\).

Step2: Identify the relevant values from the table

From the table, the number of people who are 35 - 44 years of age and neither more nor less likely (\(A\cap B\)) is \(n(A\cap B) = 201\). The number of people who are 35 - 44 years of age (\(B\)) is \(n(B)=535\).

Step3: Calculate the probability

Substitute the values into the formula: \(P(A|B)=\frac{201}{535}\approx 0.376\)

Answer:

\(0.376\)