At a certain gas station, 40% of the customers use regular gas (?A?1), 35% use plus gas (?A?2), and 25% use premium (?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 using premium, 50% fill their tanks. a. ?What is the probability that the next customer will request plus gas and fill the tank (A2?B)? b.? hat is the probability that the next customer fills the tank? c. ?If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?

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