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A few years ago, a survey commissioned by The World Almanac and Maturity News Service reported that 51% of the respondents did not believe the Social Security system will be secure in 20 years. Of the respondents who were age 45 or older, 70% believed the system will be secure in 20 years. Of the people surveyed, 57% were under age 45. One respondent is selected randomly. a. What is the probability that the person is age 45 or older?

b. What is the probability that the person is younger than age 45 and believes that the Social Security system will be secure in 20 years?

c. If the person selected believes the Social Security system will be secure in 20 years, what is the probability that the person is 45 years old or older?

d. What is the probability that the person is younger than age 45 or believes the Social Security system will not be secure in 20 years?

Answer :

Answer:

Step-by-step explanation:

a) the probability that the person is age 45 or older

=[tex]100-57 =43%\\=0.43[/tex]

b) the respondents did not believe the Social Security system will be secure in 20 years[tex]=51% = 0.43* (1-0.7)+0.57*x\\0.51-0.129 = 0.57x\\x = 0.381/0.57 = 0.6684[/tex]

i.e. prob that under 45 does not believe in this is 0.6684

the probability that the person is younger than age 45 and believes that the Social Security system will be secure in 20 years

=[tex]0.57(10.6684)\\=0.3810 [/tex]

c) the probability that the person is 45 years old or older given that the person selected believes the Social Security system will be secure in 20 years=Prob for both as in part b/prob he believes in SSS

=[tex]\frac{0.3810}{0.49}[/tex]

=0.778

d) As shown above 0.6684

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