4 Suppose that 55% ofall adults regularly consume coffee, 45% regularly consume

Question

4 Suppose that 55% ofall adults regularly consume coffee, 45% regularly consume soda, and 70% regularly consume at least one of the 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 regularly consumes coffee given that they regularly consumes soda? c. Let C = the event that a person drinks coffee and let S = the event that a person drinks soda (Diet Coke ofcourse). Circle the correct statement. (Note-mutually exclusive means the same as disjoint.) i. C and S are not mutually exclusive and they are not independent ii. C and S are not mutually exclusive but they are independent iii. C and S are mutually exclusive but they are not independent iv. C and S are mutually exclusive and they are independent

Explanation / Answer

Let A denote the even of consuming coffee and B denote the event of consuming soda.

Given P(A) = 0.55 P(B) = 0.45 P(A U B) = 0.7

a. P(A B) = P(A) + P(B) - P(A B)

= 0.45 + 0.55 - 0.7

= 0.3

b. P(A|B) = P(A B) / P(B)

= 0.3 / 0.45 = 0.67

c. Since neither did the values of P(A|B) and P(A) match nor did P(A B) yield 0, the events are neither independent nor mutually exclusive.

The correct answer is i.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.