Respuesta :
Answer: a) 50%, b) 25%.
Step-by-step explanation:
Since we have given that
Probability of all adults regularly consume coffee P(C) = 65%
Probability of all adults regularly consume soda P(S) = 60%
Probability of all adults regularly either one of them P(C ∪S) = 75%
According to question, we get that
(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
[tex]P(C\cup S)=P(C)+P(S)-P(C\cap S)\\\\0.75=0.65+0.60-P(C\cap S)\\\\0.75=1.25-P(C\cap S)\\\\P(C\cap S)=1.25-0.75=0.5=50\%[/tex]
(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
P(C∪S)'=1-P(C∪S)
[tex]P(C\cup S)'=1-0.75=0.25=25\%[/tex]
Hence, a) 50%, b) 25%.
Answer:
(a) 0.50 or 50%
(b) 0.25 or 25%
Step-by-step explanation:
We are given that;
Probability of adults that regularly consume coffee, P(C) = 0.65
Probability of adults that regularly consume carbonated soda, P(S) = 0.60
Probability of adults that regularly consume at least one of these two products, P(C [tex]\bigcup[/tex] S) = 0.75
(a) Probability that a randomly selected adult regularly consumes both coffee and soda is given by P(C [tex]\bigcap[/tex] S) ;
P(C [tex]\bigcup[/tex] S) = P(C) + P(S) - P(C [tex]\bigcap[/tex] S)
0.75 = 0.65 + 0.60 - P(C [tex]\bigcap[/tex] S)
P(C [tex]\bigcap[/tex] S) = 1.25 - 0.75 = 0.50
Therefore, the probability that a randomly selected adult regularly consumes both coffee and soda is 0.50 or 50%.
(b) Probability that a randomly selected adult doesn't regularly consume at least one of these two products = P(C [tex]\bigcup[/tex] S)'
P(C [tex]\bigcup[/tex] S)' = 1 - P(C [tex]\bigcup[/tex] S) = 1 - 0.75 = 0.25 or 25% .
