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At a certain gas station, 40% of the customers use regular
Chapter 3, Problem 59E(choose chapter or problem)
At a certain gas station, 40% of the customers use regular gas(\(A_1\)), 35% use plus gas (\(A_2\)) and 25 % usepremium (\(A_3\)). 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 premium, 50% fill their tanks.
a) What is the probability that the next customer will request plus gas and fill their tank ?
b) What is the probability that the next customer fills the tank ?
c)If the next customer fills the tank, what is the probability that the regular gas is requested? Plus ?Premium?
Questions & Answers
QUESTION:
At a certain gas station, 40% of the customers use regular gas(\(A_1\)), 35% use plus gas (\(A_2\)) and 25 % usepremium (\(A_3\)). 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 premium, 50% fill their tanks.
a) What is the probability that the next customer will request plus gas and fill their tank ?
b) What is the probability that the next customer fills the tank ?
c)If the next customer fills the tank, what is the probability that the regular gas is requested? Plus ?Premium?
ANSWER:Answer : Step 1 : Given,at a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A 3). P(A )1= 40 = 0.40 100 P(A )2= 35 = 0.35 100 P(A ) = 25 = 0.25 3 100 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. Then, P( B ) = 30 = 0.3 A1 100 B 60 P( A ) = 100 = 0.4 2 P( B ) = 50 = 0.5 A3 100 Therefore, B P(A 1B) = P(A 1 P( )A1 P(A 1B) = (0.40) (0.3) P(A B) = 0.12 1 B P(A 2B) = P(A 2 P( )A2 P(A B) 2 = (0.35) (0.60) P(A 2B)= 0.21 P(A B) = P(A ) P( )B 3 3 A3 P(A B)= (0.25) (0.50) 3 P(A 3B) = 0.125 a). Let the probability that the next customer will request plus gas and fill the tank. 2 Here A2B = 0.14