Question

5. (5 Marks) At a certain gas station, 60% of the customers use Regular gas (A1), 20% use Plus gas (A2), and 20% use Premium (A3). Of those customers using regular gas, only 45% fill their tanks (event B). Of those customer using plus, 50% fill their tanks, whereas of those using premium, 55% fill their tanks. If the next customer fills the tank, what is the probability that Plus gas is requested?

Answer 1

Given - Probability of customores use regular gas.P(A)=0.6 Probability of customers using plusgas: PA2)- 0.2 probability of customers using promiumges PA3) = 0.2 condition probability of full tank. PLB/A,) =0.445 PIB/A2) =0.5 PLD/A3)=0.55 solution Here we use bayer theorem because PLA+P(A2) HP(A3)= 0.6+0.270.2=1 therefore, according to baye's theorem

9f the best customeu fills the thak, probability that plus gas is required is given as PLA₂B). PEAD) Play PLA). P(BIA) + P(A2) · P(B|A2) + Plaz) • P(B/A3) 0.2 x 0.5 10.6x0.45) +(0.280-8) + (0.230-55) 0.10 0.270 +10 + Oil 10 0-1 0.48 = 0.20833 0.208