Graded Problem 2.6

a

0, you cannot have a sum of 1 with two die ##b You can get a sum of 5 by getting a (1,4), (2,3), (4,1), (3,2). The probability of rolling a 5 is 4/36 or .111 ##c You can get a sum of 12 by adding (6,6). This only occures once while rolling 2 dice. The probability is 1/36

Graded Problem 2.8

a.

No, there are American’s that either speak a foreign languare or are living below the poverty line. They are not mutually exclusive ##b. see seperate document ##c. 10.4% ##d. 26.9% ##e. 64.7% ##f. P(below pov line, speaks foreign language) = .042 P(speaks foreign language) x P(below pov lin) = .207 * .104 =.0215 The events are dependant.

Graded Problem 2.20

a.

P(A or B) = P(A) + p(B) - P(A & B)

A <- (114/204)
B <- (108/204)
AB <- (78/204)
ans <- A + B - (AB)
ans
## [1] 0.7058824

b.

78/204
## [1] 0.3823529

c.

19/54
## [1] 0.3518519
11/36
## [1] 0.3055556

d.

The events are dependent based on the Baynes’ Theorum.

Graded Problem 2.30

a.

HC <- (28/95)
PBF <- (59/94)
HC*PBF
## [1] 0.1849944

b.

FB <- (72/95)
HCB <- (28/94)
FB*HCB
## [1] 0.2257559

c.

fiction <- (72/95)
hardcover <- (28/95)
fiction*hardcover
## [1] 0.2233795

d.

The results are very similar because a single book counts for a small change in probability for a large sample size.

Graded Problem 3.38

onebag <- 25
twobags <- 35+25
nocheck <- .54
onecheck <- .34
twocheck <- .12

a.

probability <- matrix(c(0, 25, 60, .54, .34, .12, 0*.54, 24*.34, 60*.12), ncol = 3)
colnames(probability) <- c("fee", "prob", "fee * prob")
rownames(probability) <- c("no checked", "1 check", "2 check")
probability.table <- as.table(probability)
probability.table
##              fee  prob fee * prob
## no checked  0.00  0.54       0.00
## 1 check    25.00  0.34       8.16
## 2 check    60.00  0.12       7.20

expected value of each customer

EV <- ((0*54)+(25*.34)+(60*.12))
EV
## [1] 15.7
revenue <- c(0, 8.16, 7.20)
sd(revenue, na.rm=FALSE)
## [1] 4.459955

b.

r120 <- ((120*0)+(120*8.16)+(120*7.20))
r120
## [1] 1843.2
newrev <- c(0, 979.2, 864)
sd(newrev, na.rm=FALSE)
## [1] 535.1946

This assumes that all there is no change in the percentage of people who use carry on, check one bag, or check two bags. #Graded Problem 2.44 ##a. There is a high percentage (53.4%) of people who make between $25,000 and $64,999 per year. Almost 10% of people make more than $100,000 per year. Only 2.2% of people make below $10,000 ##b. 62.2% ##c.

(.59)*(.622)
## [1] 0.36698

d.

(.718)*(.622)
## [1] 0.446596

The assumption is not correct. This number is a higher percentage of women making under $50k than assuming there is an equal chance.