Question

The management of Acme Business Park requires each business to have its own Web site. A business may either create a Web site utilizing one of several free Web site building services or contract to have a Web site consulting firm create the site. It was determined that 30% of businesses would use the free Web site building option and that 8 % of all businesses will eventually have both a “free” and a “contracted for” Web site in operation. Assuming that 100% of these businesses are connected to the Web: 1. What percent will have only a “contracted for” Web site? 2. What is the probability that a business will have a free Web site given that they already have a “contracted for” web site?

Answer 1

1.

Let F and C be the event that businesses will have “free” and a “contracted for” Web site in operation respectively.

P(F) = 0.3

P(F and C) = 0.08

P(F or C) = 1

We know that,

P(F or C) = P(F) + P(C) - P(F and C)

1 = 0.3 + P(C) - 0.08

=> P(C) = 1 - 0.3 + 0.08 = 0.78

Percent will have only a “contracted for” Web site = P(C) = 0.78 = 78%

2.

Probability that a business will have a free Web site given that they already have a “contracted for” web site

= P(F | C) = P(F and C) / P(C)

= 0.08 / 0.78

= 0.1025641