Respuesta :
(i) The probability of a randomly selected adult consuming both coffee and soda regularly will be given by: P(A ∩ B) = 0.30.
(ii) The probability of a randomly selected adult not consuming at least one out of coffee and soda regularly is given by: P((A ∪ B)') = 0.25.
What is probability of an event?
The probability of an event refers to the chances of occurrence of an event.
P(E) = Chances of occurrence of an event E = [tex]\frac{Number Of Favorable Outcomes Of Event E}{Total Number Of Possible Outcomes}[/tex]
Step-by-step explanation:
Given:
- 40% of all adults regularly consume coffee,
- 65% regularly consume carbonated soda,
- 75% regularly consume at least one of these two products.
Now let A = Event that an adult consumes coffee
B = Event that an adult consumes carbonated soda.
Then,
- P(A) = probability of the occurrence of A = 0.40
- P(B) = 0.65
- P(A ∪ B) = 0.75
(i): Now, we know that:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
=> P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
∴ P(A ∩ B) = 0.40 + 0.65 - 0.75 = 0.30
Hence, the probability of a randomly selected adult consuming both coffee and soda regularly is 0.30.
A(ii): Now, we know that:
P((A ∪ B)') = 1 - P(A ∪ B)
∴ P((A ∪ B)') = 1 - 0.75 = 0.25
Hence, the probability of a randomly selected adult not consuming at least one out of coffee and soda regularly is 0.25.
To learn more about the probability of an event, refer to the given link:
https://brainly.com/question/7965468
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