Data 605 - Assignment 6

Question 1

Total number of marbles = 54+9+75 = 138

Probabilty of red marble = \(\frac{54}{138}\) Probabilty of blue marble = \(\frac{75}{138}\)

Probability or red or blue marble = \(\frac{54}{138} + \frac{75}{138} = \frac{43}{46}\)

Answer = 0.9348

Question 2

Total number of balls = 19+20+24+17 = 80

Probabilty of red ball = \(\frac{20}{80}\)

Answer = 0.2500

Question 3

Let F represent not male and NP represent not parents:

P(F or NP) = P(F) + P(NP) - P(F and NP)

P(F) = Total Non Males/Total Customers = (228+79+252+97+72)/1399 = 728/1399

P(NP) = Total Not Parents/Total Customers = (81+228+116+79+130+97+129+72)/1399 = 932/1399

P(F and NP) = (228+79+97+72)/1399 = 476/1399

P(F or NP) = 728/1399 + 932/1399 - 476/1399 = 1184/1399

Answer = 0.8463

Question 4

The events are Dependent (A)

Question 5

8C3 X 7C3 x 3C1

Ans <- choose(8,3) * choose(7,3) * choose(3,1)
Ans

## [1] 5880

Question 6

The events are independent (B)

Question 7

14P8

Ans = 121,080,960

Question 8

Total possible combinations = 22C4

Probability of 1 orange = 4C1 / 22C4

Probability of 3 green = 9C3/22C4

total <- choose(22,4)

Ans = choose(4,1) * choose(9,3) / total
Ans

## [1] 0.04593301

Question 9

Ans = factorial(11)/factorial(7)
Ans

## [1] 7920

Question 10

33% of subscribers to a fitness magazine are 34 years or younger

Question 11

Part A

Prob3 <- dbinom(3, size=4, prob=0.5)
Not3 <- 1 - Prob3

expValue = (Prob3 * 97) - (Not3 * 30) 
expValue

## [1] 1.75

Part B

Ans = 559*1.75
Ans

## [1] 978.25

Question 12

Part A

Prob4 <- pbinom(4, size=9, prob=0.5)
Not4 <- 1- Prob4

expvalue = (23 * Prob4) - (26*Not4)
expvalue

## [1] -1.5

Part B

Ans = 994 * -1.5
Ans

## [1] -1491