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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:
1. P(AuB)2. p(AuB')3. P(A'uB')

Respuesta :

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Answer:

1.  P(AuB) = 0.85

2.  P(AuB') = 0.4

3.  P(A'uB') = 0.8

Step-by-step explanation:

Given that;

There are four different color.

P(A) i.e the event that the design color is red will be; [tex]\frac{1}{4}[/tex]

= 0.25

P(B)  i.e the event that the font size is not the smallest one, = [tex]\frac{4}{5}[/tex]

=0.8

1).

Using Addition Rule;

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

P(AnB) = P(A) × P(B)

= 0.25 × 0.8

= 0.2

∴

P(AuB)= 0.25 + 0.8 - 0.2

= 0.85

Thus, the probability that A union B [ P(AuB) ]  is 0.85.

2).

Using Addition Rule;

P(AuB') = P(A) + P(B') +  P(AnB')

Here, we are asked to look for the Probability of A union B compliment.

The probability value for complementary event (B) is,

[tex]P\left( {B'} \right) = 1 - P\left( B \right)[/tex]

As such; Since P(B) = 0.8

[tex]P\left( {B'} \right) = 1 - P\left( 0.8 \right)[/tex]

[tex]P\left( {B'} \right) = 0.2[/tex]

P(AnB') = P(A) × P(B')

P(AnB') = 0.25 × 0.2

P(AnB') =  0.05

∴

P(AuB') can now be calculated as;

= P(A) + P(B') -  P(AnB')

= 0.25 + 0.2 - 0.05

= 0.4

Thus, the probability of A union B complement [ P(AuB') ] = 0.4.

3).

P(A'uB') = P(AnB)'      (according to DeMorgan's Rule)

P(A'uB') = 1 - P(AnB)

From above P(AnB) = 0.2

∴

P(A'uB') = 1 - 0.2

P(A'uB') = 0.8

Thus, the probability of A complement union B complement [ P(A'uB') ] = 0.8

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