Question

A survey about social media reported that 76​% of B2B marketers​ (marketers that focus primarily on attracting​ businesses) plan to increase their use of social​ media, as compared to 55​% of B2C marketers​ (marketers that primarily target​ consumers). The survey was based on 1,351 B2B marketers and 1,658 B2C marketers.

a. What is the probability that a randomly selected respondent plans to increase use of social​ media?

​(Round to three decimal places as​ needed.)

b. What is the probability that a randomly selected respondent is a B2C​ marketer?

​(Round to three decimal places as​ needed.)

c. What is the probability that a randomly selected respondent plans to increase use of social media or is a B2C​ marketer?

​(Round to three decimal places as​ needed.)

Answer 1

data	increase social media	do not increase social media	total
B2B	0.76	0.24	1.00
B2C	0.55	0.45	1.00

Contingency table as per data:

data	increase social media	do not increase social media	total
B2B	1026.76	324.24	1351
B2C	911.9	746.10	1658
Total	1938.66	1070.34	3009

(a) P(increase social media) = 1938.66 / 3009 = 0.644

(b) P(B2C) = 1658 / 3009 = 0.551

(c) P(increase social media or B2C) = P(increase social media) + P(B2C) - P(increase social media and B2C)

P(increase social media or B2C) =1938.66 / 3009 + 1658/3009 - 911.9/3009

P(increase social media or B2C) = 2684.76 / 3009

P(increase social media or B2C) = 0.892