To find the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country," given the individual is 45 to 54 years of age, follow these detailed steps:
1. Identify the relevant values from the contingency table.
The total number of individuals aged 45 to 54 in the survey:
[tex]\[
\text{Total (45-54)} = 583
\][/tex]
The number of individuals aged 45 to 54 who are more likely to buy a product emphasized as "Made in our country":
[tex]\[
\text{More likely (45-54)} = 395
\][/tex]
2. Determine the conditional probability.
The conditional probability [tex]\( P(A|B) \)[/tex] is defined as the probability of event A occurring given that event B has occurred, and it can be calculated using the formula:
[tex]\[
P(\text{More likely}|\text{45-54}) = \frac{\text{Number of individuals more likely (45-54)}}{\text{Total individuals (45-54)}}
\][/tex]
3. Substitute the known values into the formula.
[tex]\[
P(\text{More likely}|\text{45-54}) = \frac{395}{583}
\][/tex]
4. Calculate the probability.
[tex]\[
P(\text{More likely}|\text{45-54}) \approx 0.6775300171526587
\][/tex]
5. Round the probability to three decimal places.
[tex]\[
P(\text{More likely}|\text{45-54}) \approx 0.678
\][/tex]
Therefore, the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country," given the individual is 45 to 54 years of age, is approximately [tex]\( 0.678 \)[/tex].
