The us energy department states that 60% of all us households have ceiling fans. in addition, 29% of all us households have an outdoor grill. suppose 13% of all us households have both a ceiling fan and an outdoor grill. a us household is randomly selected.

a) what is the probability that the household has a ceiling fan or an outdoor grill?
b) what is the probability that the household has neither a ceiling fan nor an outdoor grill?
c) what is the probability that the household does not have a ceiling fan and has an outdoor grill?
d) what is the probability that the household does have a ceiling fan and does not have an outdoor grill?

For the development of this problem we will use the basic concept of Probability and relation of sets.

Our values are:

PART A ) What is the probability that the household has a ceiling fan or an outdoor grill?

PART B) What is the probability that the household has neither a ceiling fan nor an outdoor grill?

PART c) What is the probability that the household does not have a ceiling fan and does have an outdoor grill?

PART D) What is the probability that the household does have a ceiling fan and does not have an outdoor grill?

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .