Question

The US Census Bureau reports that the median family income for all US families during the year 2019 was $75500. Suppose 4 families are surveyed and asked where or not their income exceeds $75500.

a) List the points in the sample space

b) Identify the simple events in each sample space.

i. At least had 2 incomes exceeding $75500

ii. Exactly 2 had incomes exceeding $75500

iii. Exactly 1 had incomes less than or equal to $75500

Answer 1

Let Y be the event that a family have income that exceeds $75500 and say 'Yes'. Let N be the event that the response is N.

a) Sample space = {YYYY, YYYN, YYNY, YNYY, NYYY, YYNN, YNNY, NNYY, YNYN, NYNY, NYYN, NNNY, NNYN, NYNN, YNNN, NNNN}

b) i. At least 2 had income exceeding $75500 = {YYYY, YYYN, YYNY, YNYY, NYYY, YYNN, YNNY, NNYY, YNYN, NYNY, NYYN}

ii. Exactly 2 had income exceeding $75500 = {YYNN, YNNY, NNYY, YNYN, NYNY, NYYN}

iii. Exactly 1 had income less than or equal to $75500 = {YYYN, YYNY, YNYY, NYYY}