3.15 a. There are four criteria, and for each criteria a farmer can be categorized as either “likely” or “unlikely”. You might think of the sample space as something similar to the sample space of flipping four coins. Thus, there are 2⁴ =16 classifications (outcomes). Letting each of the criteria be denoted by the numbers one through four, and each of the two possible ratings on the criteria (likely and unlikely) be denoted by “L” and “U”, the 16 classifications are as follows:

	1L	2L	3L	4L
				4U
			3U	4L
				4U
		2U	3L	4L
				4U
			3U	4L
				4U
	1U	2L	3L	4L
				4U
			3U	4L
				4U
		2U	3L	4L
				4U
			3U	4L
				4U

That is, the classifications are: {[1L,2L,3L,4L], [1L,2L,3L,4U], [1L,2L,3U,4L], [1L,2L,3U,4U],…, [1U,2U,3U,4L], [1U,2U,3U,4U]}.

b. 1/16

c. 5/16 (represented by the five “highlighted” branches in the tree diagram above).

3.24 First, convert the percentages in the table to probabilities by dividing the percent by 100%.

a. P(A) = .259 + .169 + .115 = .543

P(B) = .003

P(C) = .037 + .078 + .016 + .002 + .047 + .027 = .207

P(D) = .414

b. P(A È D) = .156 + .094 + .043 = .293

P(A Ç D) = P(A) + P(B) - P(A È D) =.543+.414-.293=.664

c. A^c: (The worker is under 40}

B^c:(The worker is 20 or older or is not part-time}

D^c:{The worker is not part-time}

d. P(AC) =1 - P(A) = 1 - .543 = .457

P(BC) =1 - P(B) = 1 - .003 = .997

P(DC) =1 - P(D) = 1 - .414 = .586

3.42 a.

b.

c.

d.

e. No. If A and B are independent, then P(A|B) = P(A). Here, P(A|B)¹P(A) (0.3601¹0.4094). Thus, A and B are not independent.

3.58 To draw a random sample of 1,000 households from 534,322, we will number the households from 1 to 534,322. Then, starting in an arbitrary position in Table I, Appendix B, we will select 6-digit numbers by proceeding down a column. We will continue selecting numbers until we have 1,000 different 6-digit numbers, eliminating 000000 and any numbers between 534,323 and 999,999.