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IrinaVladis [17]
3 years ago
8

A few years ago, a survey commissioned by The World Almanac and Maturity News Service reported that 51% of the respondents did n

ot 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.Construct a probability matrix for this problem.
Mathematics
1 answer:
slamgirl [31]3 years ago
6 0

Answer:

Age    |    Believe   |   Not believe  |   Total

<45     |    0.148      |        0.422       |   0.570

>45     |    0.301      |        0.129        |   0.430

Step-by-step explanation:

We have to construct a probability matrix for this problem.

Of the people surveyed, 57% were under age 45. That means that 43% is over age 45.

70% of the ones who were 45 or older, believe the Social Security system will be secure in 20 years.

The Believe proportion is 51%.

Then, the proportion that believe and are under age 45 is:

0.51=P(B;

We can now construct the probability matrix for one respondant selected randomly:

P(45\&NB)=0.43*(1-0.7)=0.43=0.3=0.129

Age    |    Believe   |   Not believe  |   Total

<45     |    0.148      |        0.422       |   0.570

>45     |    0.301      |        0.129        |   0.430

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