Cable Services Watched: Female Married PrincipalShopper, % Detail Female Not Mar
ID: 3072247 • Letter: C
Question
Cable Services Watched:
Female Married PrincipalShopper, % Detail
Female Not Married PrincipalShopper, % Detail
Male Married PrincipalShopper, % Detail
Male Not Married PrincipalShopper, % Detail
A&E
20%
18%
22%
22%
Animal Planet
16%
16%
21%
25%
Cartoon Network
12%
12%
16%
18%
CNN
21%
23%
24%
22%
Comedy Central
88%
66%
13%
11%
E! (Entertainment Television)
17%
21%
23%
26%
ESPN
18%
17%
47%
45%
Fox News Channel
27%
27%
29%
31%
Lifetime
20%
19%
10%
12%
Syfy
77%
10%
15%
17%
Total Est (000s)
47,880
37,611
17,234
11,637
How many unmarried male shoppers might I possibly reach with advertising campaigns for the following combinations of TV shows? Keep in mind, we want to avoid "double counting" males who may watch both channels. For simplicity, though, assume that the chance a male watches one cable channel does not influence the chances they will watch a different channel.
When two events are considered to be unrelated to one another, the probability of them BOTH happening is just "Probability of Event
A"times×"Probability
of Event B". This is represented as
"Upper P left parenthesis Upper A intersect Upper B right parenthesisP(AB)".
The combined probability of the events is "Probability of Event
A"plus+"Probability
of Event
B"minus"Upper P left parenthesis Upper A intersect Upper B right parenthesisP(AB)".
Multiply the the combined probability of watching both channels by the total number of unmarried male shoppers. Use the provided table above to answer the question.
Fill in the table below. (Round to the nearest whole number.)
Number of unmarried male shoppers watching both channels
(000s)
A&E and Animal Planet
4,829
ESPN and SyFy
(---------
CNN and Fox News
Among married principal shoppers, (---------)1 is the ratio of females to males. (Round to two decimal places.)
Among married principal shoppers who watch Comedy Central, (-------------):1 is the ratio of females to males. (Round to two decimal places.)
The percentage of all SyFy-watching principal shoppers that are married is calculated as follows:
% of all SyFy dash watching Principal Shoppers are Married = equals StartFraction Female Married Pricipal Shopper Subscript SyFy + Male Married Pricipal Shopper Subscript SyFy Over All Principal Shoppers Subscript SyFy EndFraction% of all SyFy
Cable Services Watched:
All Principal Shoppers
Est (millions)
Female Married Principal Shopper Est (millions)
Male Married Principal Shopper Est (millions)
A&E
57.1
14.6
5.4
Animal Planet
63.1
15.4
6.7
Cartoon Network
22.2
5.9
2.1
CNN
43.5
9.4
4.1
Comedy Central
14.5
2.6
2.2
E! (Entertainment Television)
24.4
6.7
1.6
ESPN
58.1
10.8
7.2
Fox News Channel
54.1
12.5
4.8
Lifetime
31.1
9.9
1.3
Syfy
37.6
8.4
4.4
Totals
206.9
47.1
21.1
(---------------) % of all SyFy-watching principal shoppers are married. (Round to two decimal places.)
Approximately speaking, do married men or married women principal shoppers say they watch more of the cable channels listed here?
Fill in the table below. (Round to two decimal places.)
Avg. Channels Watched by Women Married.
Avg. Channels Watched by Men Married
(-----------)
(----------)
Cable Services Watched:
Female Married PrincipalShopper, % Detail
Female Not Married PrincipalShopper, % Detail
Male Married PrincipalShopper, % Detail
Male Not Married PrincipalShopper, % Detail
A&E
20%
18%
22%
22%
Animal Planet
16%
16%
21%
25%
Cartoon Network
12%
12%
16%
18%
CNN
21%
23%
24%
22%
Comedy Central
88%
66%
13%
11%
E! (Entertainment Television)
17%
21%
23%
26%
ESPN
18%
17%
47%
45%
Fox News Channel
27%
27%
29%
31%
Lifetime
20%
19%
10%
12%
Syfy
77%
10%
15%
17%
Total Est (000s)
47,880
37,611
17,234
11,637
Explanation / Answer
Answer to question# 1)
Probability for unmarried male couples:
P(A&E and Animal planet) = P(A&E)*P(Animal planet)
P(A&E and Animal planet) = 0.22 * 0.25 = 0.055
.
P(A&E OR Animal Planet) = P(A&E) + P(Animal planet) – P(A&E AND Animal planet)
P(A&E OR Animal Planet) =0.22 +0.25 -0.055
P(A&E OR Animal Planet) = 0.415
Thus total number of unmarried males : 0.415*11637 = 4829
.
P(ESPN or SyFy) = P(ESPN) + P(Syfy) – P(ESPN and Syfy)
P(ESPN or SyFy) = 0.45 +0.17 – 0.45*0.17
P(ESPN or SyFy) = 0.5435
Thus total number of unmarried males = 0.5435 *11637 = 6324
.
P(cartoon or E!) = P(Cartoon) + P(E!) - P(cartoon AND E!)
P(Cartoon or E!) = 0.18 + 0.26 – 0.18*0.26
P(Cartoon or E!) = 0.3932
Thus total number of unmarried males = 0.3932 *11637 = 4575
.
P(CNN or Fox) = P(CNN) + P(Fox) – P(CNN and Fox)
P(CNN or Fox) = 0.22 + 0.31 – 0.22*0.31
P(CNN or Fox) =0.4618
Thus total number of unmarried males = 0.4618 *11637 = 5373