Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two types of drinks.
(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
(c) What is the probability that a randomly selected adult regularly consumes coffee but does not regularly consume soda?

a) The probability that a randomly selected adult consumes both cofee and soda is 0.3

b) the probability that a randomly selected adult doesnt consume at least one of cofee and soda is 0.7

c) The probability that a randomly selected adult consumes cofee but not soda is 0.25

Step-by-step explanation:

Lets pick a random adult and use the random variables

C = the adult consumes cofee

S = the adult consumes sodaa

we have that

P(C) = 0.55

P(S) = 0.45

P(C U S) = 0.7

a) We know that

0.7 = P(C U S) = P(C) + P(S) - P(C ∩ S) = 0.55 + 0.45 - P(C ∩ S)

Therefore

P(C ∩ S) = 0.55+0.45-0.7 = 0.3.

and as a consecuence, the probability that a randomly selected adult consumes both cofee and soda is 0.3.

b) The event 'a randomly selected adult doesnt consume at least one of the 2 products' is the complementary event of 'the adult consumes both cofee and soda', thus, the probability of this event is 1-P(C ∩ S) = 1 - 0.3 = 0.7.

c) Remember that

0.55 = P(C) = P(C ∩S) + P(C ∩ S^c) = 0.3 + P(C ∩ S^c)

Where S^c means that the adult doesnt consume soda. We can conclude that

P(C ∩ S^c) = 0.55-0.3 = 0.25

The probability that a randomly selected adult consumes cofee but not soda is 0.25.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

hi im bob : l

step-by-step explanation: