The Bureau of Census reports that the median family income in California during

Question

The Bureau of Census reports that the median family income in California during the last year was $65,000. Suppose that four families are surveyed and that each one reports whether its income exceeded the reported medium for that year.

1. List the sample points.

2. Identify the following simple events:

A: At least two families had incomes exceeding the median

B: Exactly two families had incomes exceeding the median

C: Exactly one family had income less than or equal to the median

3. Assign probabilities to the simple events and find P(A), P(B), and P(C).

Explanation / Answer

Let Y be an outcome denoting whether a family reports that their income exceeded the reported median for that year.
Let N be an outcome denoting whether a family reports that their income is less than or equal to the reported median for that year.

(1) The sample points are listed here.
Sample points = {NNNN, NNNY, NNYN, NNYY, NYNN, NYNY, NYYN, NYYY, YNNN, YNNY, YNYN, YNYY, YYNN, YYNY, YYYN, YYYY}.

(2) A = {NNYY, NYNY, NYYN, NYYY, YNNY, YNYN, YNYY, YYNN, YYNY, YYYN, YYYY}.
B = {NNYY, NYNY, NYYN, YNNY, YNYN, YYNN}.
C = {NYYY, YNYY, YYNY, YYYN}.

(3) P(A) = 11/16.
P(B) = 6/16.
P(C) = 4/16.
C = {

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