Suppose that 55% of all adults regularly consume coffee, 45% regularly consume car- bonated soda, and 70% regularly consume at least one of these two products.

(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?

Expert Solution

solution

We have P(coffee )=0.55 and P( soda)=0.45

P( coffee or soda)=0.7

(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?

=>P(coffee and soda)= P(C\( \cap \)B)=P(C)+P(S)-P(C\( \cup \)S)

= 0.55+0.45-0.7

=0.3

(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

=>P(\( \overline {C\cup S} \))=1-P(C\( \cup \)S)=1-0.7=0.3

Answer

(a).P(coffee and soda) is P(C\( \cap \)S)=0.3

(b). P(coffee or soda) is P(\( \overline {C\cup S} \))=0.3

SUN BUNRA answered 2 years ago

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