Question

The contingency table below shows the results of a survey of video viewing habits by age.

		Video Viewing Platform Preferred
Viewer Age	Mobile/Laptop Device				TV Screen				Row Total
18–34		35				38				73
35–54		9				9				18
55+		3				6				9
Column Total		47				53				100

Find the following probabilities or percentages:

(a) Probability that a viewer is aged 18–34. (Round your answer to 2 decimal places.)

Probability           

(b) Probability that a viewer prefers watching videos on a TV screen. (Round your answer to 2 decimal places.)

Probability           

(c) Percentage of viewers who are 18–34 and prefer videos on a mobile or laptop device.

Percentage of viewers            %

(d) Percentage of viewers aged 18–34 who prefer videos on a mobile or laptop device. (Round your answer to 2 decimal places.)

Percentage of viewers            %

(e) Percentage of viewers who are 35–54 or prefer videos on a mobile or laptop device.

Percentage of viewers            %

Answer 1

Solution :

From given table ,

(a) => P(aged 18 - 34) = 73/100 = 0.73

=> Probability that a viewer is aged 18–34 is 0.73

  
(b) => P(TV screen) = 53/100 = 0.53

=> Probability that a viewer prefers watching videos on a TV screen is 0.53

  
(c) => P(18 – 34 and prefer videos on a mobile or laptop device) = 35/100 = 0.35 = 35%

=> Percentage of viewers who are 18 – 34 and prefer videos on a mobile or laptop device is 35%

  
(d) => P(prefer videos on a mobile or laptop device/18 – 34) = P(mobile or laptop device ∩ 18 - 34)/P(18 - 34)

= 35/73

= 0.4795

= 47.95%

=> Percentage of viewers aged 18 – 34 who prefer videos on a mobile or laptop device is 47.95%

(e) => P(35 – 54 or prefer videos on a mobile or laptop device)

= P(35 - 54) + P(prefer videos on a mobile or laptop device) - P(35 – 54 and prefer videos on a mobile or laptop device)

= 18/100 + 47/100 - 9/100

= 0.18 + 0.47 - 0.09

= 0.56

= 56%

=> Percentage of viewers who are 35–54 or prefer videos on a mobile or laptop device is 56%