Question

A web ad can be designed from four different colors, three font types, five sizes, three images, and five text phrases. A specific design is randomly generated by the web server when you visit the site. Let A denote the event that the design color is red and let B denote the event that the font size is not the smallest one. Use the addition rilues to calculate the following probabilities:a. P(AuB)b. p(AuB')c. P(A'uB')

Answer 1

a. 3/4

b. 1/2

c. 5/6

Explanation:

From the question, We are given that:

4 different colours, 3 different font types, 5 sizes, 3 images, 5 text phrases.

If event A is the event that the design color is red, then:

P(A) = 1/4

P(A') = 1 - 1/4 = 3/4.

If event B is the event that the font size is not the smallest one, then:

P(B) = 2/3

P(B')= 1 - 2/3 = 1/3.

P(AnB) = 1/4 * 2/3 = 2/12=1/6

P(AnB')=1/4 * 1/3 = 1/12

P(A'nB') = 3/4 * 1/3=1/4

Solving the questions,

a. P(AuB) = P(A) + P(B) - P(AnB)

P(AuB) =(1/4) + (2/3) -(1/6)

P(AuB) = 9/12

P(AuB) = 3/4

b. P(AuB') = P(A) + P(B') - P(AnB')

P(AuB') = 1/4 + 1/3 - 1/12

P(AuB') = 6/12

P(AuB') = 1/2

c. P(A'uB') = P(A') + P(B') - P(A'nB')

P(A'uB') = 3/4 + 1/3 - 1/4

P(A'uB') = 10/12

P(A'uB')=5/6