The State of Texas maintains records pertaining to the economic development of corporations in the state. From the Economic Development Corporation Report, published by the Texas Comptroller of Public Accounts, we obtained the following frequency distribution summarizing the sales tax receipts from the state's Type 4A development corporations during one fiscal year.
Receipts Frequency
$0–24,999 .......... 25
$25,000–49,999 ........ 23
$50,000–74,999 ........ 21
$75,000–99,999 ........ 11
$100,000–199,999 ....... 34
$200,000–499,999 ....... 44
$500,000–999,999 ....... 17
$1,000,000 & over ....... 32
Suppose that one of these Type 4A development corporations is selected at random. Let
A = event the receipts are less than $25,000,
B = event the receipts are between $25,000 and $49,999,
C = event the receipts are between $500,000 and $999,999,
D = event the receipts are at least $1,000,000, and
R = event the receipts are either less than $50,000 or at least $500,000.
a. Use the table and the f/N rule to find P(R).
b. Express event R in terms of events A, B, C, and D.
c. Determine P(A), P(B), P(C), and P(D).
d. Compute P(R) by using the special addition rule and your answers from parts (b) and (c). Compare your answer with that in part (a).