6- # 59 (book) 59. At a certain gas station, 40% of the customers use regular ga

Question

6- # 59 (book) 59. At a certain gas station, 40% of the customers use regular gas (Al), 35% use plus gas (A2), and 25% use premium (As). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. a. What is the probability that the next customer will request plus gas and fill the tank (A2 n B)? the tank? probability that regular gas is requested? Plus? b. What is the probability that the next customer fills c. If the next customer fills the tank, what is the Premium?

Explanation / Answer

a) P(A2nB) =P(A2)*P(B|A2) =0.35*0.60=0.21

b) P(B) =P(A1)*P(B|A1) +P(A2)*P(B|A2)+ P(A3)*P(B|A3)

=0.4*0.3+0.35*0.6+0.25*0.5=0.455

c) probability regular gas if fils the tank -P(A1|B) =P(A1)*P(B|A1) /P(B) =0.4*0.3/0.455 =0.2637

probability plus gas if fils the tank -P(A2|B) =P(A2)*P(B|A2) /P(B) =0.35*0.6/0.455 =0.4615

probability premium gas if fils the tank -P(A3|B) =P(A3)*P(B|A3) /P(B) =0.25*0.5/0.455 =0.2747

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

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