Question

The Bureau of the Census reports that the median family income for all families in the United States during the year 2003 was $43,318. That is, half of all American families had incomes exceeding this amount, and half had incomes equal to or below this amount. Suppose that four families are surveyed and that each one reveals whether its income exceeded $43,318 in 2003.(a)List the points in the sample space. (Enter your answer in set notation. Let G represent the event that a family's income is greater than $43,318, and N represent that the family's income is not greater than $43,318.)

Answer 1

{GGGG, GGGN, GGNG, GNGG, NGGG, GGNN, GNGN, GNNG, NGGN, NGNG, NNGG, GNNN, NGNN, NNGN. NNNG, NNNN}

Explanation:

4 families are surveyed and each one reveals whether its income exceeded $43,318 in 2003. Each family has two possibilities: Having an income greater than 43,318 (G), or is not greater than $43,318 (N). We have 2⁴ = 16 different outcomes.

The possible outcomes are: GGGG, GGGN, GGNG, GNGG, NGGG, GGNN, GNGN, GNNG, NGGN, NGNG, NNGG, GNNN, NGNN, NNGN. NNNG, NNNN.

Therefore the sample space is {GGGG, GGGN, GGNG, GNGG, NGGG, GGNN, GNGN, GNNG, NGGN, NGNG, NNGG, GNNN, NGNN, NNGN. NNNG, NNNN}