In a survey of 1012 adults aged 18 years and older conducted by a research compa

Question

In a survey of 1012 adults aged 18 years and older conducted by a research company, it was found that gas prices have caused financial hardship for 70% of the respondents aged 18–49 years and 65% of those who are 50 years or older. There were 762 adults aged 18–49 years and 250 adults who were 50 years or older in the survey. If a respondent in the survey selected at random reported that he or she did not experience financial hardship from gas prices, what is the probability that he or she was an adult aged 18–49 years? (Round your answer to three decimal places.)

Explanation / Answer

Lets A is group of people aged 18-49 no. 762 P(A) = 762/1012 = 0.753

Lets B is group of people aged 50+ no. 250 P(B) = 250/1012 = 0.247

Lets C is condition of financial hardship due to gas prices

D is condition of no-financial hardship due to gas prices

Probability of a person randomly selected having no-financial hardship bring in group A is P(A/D)

P(A/D) = P(A and D) / P(D) = 0.753*0.3 / (0.753*0.3 + 0.247*0.35) = 0.2259 / 0.31235 = 0.723227 ~ 0.723

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