Question

Cable Services​ Watched:	Female Married Principal​Shopper, % Detail	Female Not Married Principal​Shopper, % Detail	Male Married Principal​Shopper, % Detail	Male Not Married Principal​Shopper, % 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(A∩B)​".

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(A∩B)​".

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			(---------
Cartoon Network and​ E! (----------)

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
(-----------)	(----------)

Answer 1

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