A Web ad can be designed from four different colors, three font types, five font 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 rules to calculate the following probabilities.
A. P(A ∪ B).
B. P(A ∪ B').
C. P(A' ∪ B').

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farisfekeri farisfekeri · Answer 1 · 2020-02-07T09:05:31+01:00

The probability of A = 1/4 = 0.25

The probability of B = 4/5 = 0.80

P(A ∩ B) = P(A) * P (B) = (0.25) * (0.80) = 0.20

P(A ∩ B') = P(A) * P (B') = (0.25) * (1-0.80) = 0.05

P(A' ∩ B') = P(A') * P (B') = (1-0.25) * (1-0.80) = 0.15

Answer:

A. P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.25 + 0.80 - 0.20 = 0.85

B. P(A U B') = P(A) + (1 - P(B)) - P(A ∩ B') = 0.25 + (1-0.80) - 0.05 = 0.40

C. P(A' U B') = (1 - P(A)) + (1 - P(B)) - P(A' ∩ B') = (1-0.25) + (1-0.80) - 0.15 = 0.80