Question 1:
1a) {NNNN, NNNG, NNGN, NGNN, NNGG, NGNG, NGGN GGNN, GNGN, GNNG, GGGG,
GNNN, GGNG, GNGG, NGGG, GGGN}
b) A. {GGNN, GGGN, NGGG, GGGG, NNGG, NGNG, GNGG, GGNG, GNNG, NGGN}
B. {GGNN, NGNG, GNGN, NNGG, NGGN, GNNG}
C. {NGGG, GNGG, GGNG, GGGN}
c) probability of three events
P(At least two households had incomes above $66,800) = 10/16 = 0.625
P (exactly two households incomes above 66,800) = 6/16 = 0.375
P ( Exactly one household had an income less than or equal to $66,800) = 4/16 =
0.25
Question 2:
b) Bayes’ Theorem
P (pc | +) = p (pc ∩ +) / (+)
P (pc | +) = (p(+|PC)*(PC))/p(+|PC)+p(+|NPC)
P (pc | +) = (0.51 x 0.06) / (0.0306 + 0.8554) = 0.2656
c)
Cancer
No Cancer
Total
Positive
3,060
8,460
11,520
Negative
2,940
85,540
88,480
Total
6,000
94,000
100,000
d) P(Cancer Positive | positive total) = 3060/11520 = 0.2656
e) The amount of PSA positive men will be 11520 since its 3060 +8,460= 11,520 because
cancer positive + no cancer positive
Question 3:
a) The two questions are both complementary and mutually exclusive. The reason it is
mutually exclusive is that you can’t have both households with and without kids at the
same time. It can be also complementary because mutually exclusive events are
complementary. Having household with kids and household without kids are the only two
possibilities available.
b) The probability that a household that has no kids:
i)
no kids in household = total household - with kids household
ii)
no kids in household = 1400 - 900
iii)
no kids in household = 500
iv)
P (no kids in household) = no kids household/ total household
v)
P (no kids in household) = 500/1400
vi)
P(no kids in household) = 0.3571
c) P(household with kids) = 1-P(no kids in household)
i)
P(household with kids) = 1-0.3571
ii)
P(household with kids) = 0.6429
iii)
P (household with kids ∩ SUV) = P(household with kids) * (household SUV and
kids)
iv)
P (household with kids ∩ SUV) = (0.6429) * (0.59) = 0.3793
d) P(SUV) = P(household with kids)*(percentage suv and kids) + P(household with no
kids)* (percentage suv and no kids)
i)
P(SUV) = (0.3571)(.51) + (0.6439)(0.59) = 0.5620
e) P (no kids w/household ∩ no SUV) = P(no kids in household) * P (1-percentage of SUV
with no kids)
i)
P (no kids w/household ∩ no SUV) = 0.3571 * ( 1-0.51) = 0.1748
Question 4:
a)
Beer
Soft Drink
Wine
Total
Male
142
20
40
202
Female
38
10
20
68
Total
180
30
60
270
b) and c) shown on excel
p(male given drinks) = (male beer)/(total male) = 142/202 = 0.70
p(female given drinks) = (female beer)/(total female) = 38/68 = 0.56
d) a pattern observed is with exception of beer, twice as much men consume soft drinks and
wine compared to females. It also shows that in total, soft drinks are three times less than beers
and twice as less than wine drunk by both genders. It also shows that men are the dominant
customer gender, and they consume an exponential amount more than females when it comes
to beer