Answer: a) 30% and b) 45%
Step-by-step explanation:
Since we have given that
Probability that adults regularly consume coffee P(C) = 45% = 0.45
Probability that adults regularly consume carbonated soda P(S) = 40% = 0.40
Probability that adults regularly consume atleast one of these two products P(C∪S) = 55% = 0.55
a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
As we know that
P(C∪S ) = P(C) +P(S)-P(C∩S)
[tex]0.55=0.45+0.40-P(C\cap S)\\\\0.55=0.85-P(C\cap S)\\\\0.55-0.85=-P(C\cap S)\\\\-0.30=-P(C\cap S)\\\\P(C\cap S)=0.30=30\%[/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)'=n(U)-P(C∪S)
[tex]\\P(C\cup S)'=100-55=45\%[/tex]
Hence, a) 30% and b) 45%
