Hi, I need help with this question please At a certain gas station, 40% of the c

Question

Hi, I need help with this question please

At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (As). Of those customers using regular gas, only 40% fill their tanks (event B). Of those customers using plus, 80% fill their tanks, whereas of those using premium, 30% fill their tanks. Consider the following information on credit card usage. · 70% of all regular fill-up customers use a credit card · 50% of all regular non-fill-up customers use a credit card · 60% of all plus fill-up customers use a credit card. · 50% of all plus non-fill-up customers use a credit card. 50% of all premium fill-up customers use a credit card. 40% of all premium non-fill-up customers use a credit card. Compute the probability of each of the following events for the next customer to arrive (a tree diagram might help) (a) plus and fill-up and credit card) (b) (premium and non-fill-up and credit card) (c) (premium and credit card) (d) ffill-up and credit card) (e) credit card) (f) If the next customer uses a credit card, what is the probability that premium was requested? (Round your answer to four decimal places.,)

Explanation / Answer

a)probability =0.35*0.8*0.6=0.168

b) probability =0.25*0.7*0.4 =0.07

c) Probability =P(premium fill up and credit card+premium non fill up and credit card)

=0.25*0.3*0.5+0.25*0.7*0.4=0.1075

d) P(fill up and redit card) =P(regular fill up and credit card+plus fill up and credit card+premium fill up and credit card)=0.4*0.4*0.7+0.35*0.8*0.6+0.25*0.3*0.5=0.3175

e) credit card=P(regular fill up and credit card+plus fill up and credit card+premium fill up and credit card)+P(regular non fill up and credit card+plus nonfill up and credit card+premium nonfill up and credit card)

=0.4*0.4*0.7+0.35*0.8*0.6+0.25*0.3*0.5+0.4*0.6*0.5+0.35*0.2*0.5+0.25*0.7*0.4=0.5425

f)

P(premium|credit card) =(premium fill up and credit card+premium nonfill up and credit card)/P(credit card)

=(0.25*0.3*0.5+0.25*0.7*0.4)/0.5425=0.1982

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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