58. At a certain gas station, 40% of the customers use regular unleaded gas (A1), 35% use...

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58. At a certain gas station, 40% of the customers use regular unleaded gas (A1), 35% use extra unleaded gas (A2), and 25% use premium unleaded gas (A3).

Of those customers using regular gas, only 30% ll their tanks (event B). Of those customers using extra gas, 60% ll their tanks, whereas of those using premium, 50% ll their tanks.

a. What is the probability that the next customer will request extra unleaded gas and ll the tank

(A2 B)?

b. What is the probability that the next customer lls the tank?

P1A ¨ B 0 C2.

P1A ´ B 0 C2 P1A 0 C2 P1B 0 C2

P1B¿ 0 A2 P1B 0 A2 P1B2, P1B¿ 0 A2 P1B¿ 2.

P1A 0 B2 P1A¿ 0 B2 1.

P1A1 ¨ A2 ¨ A3 0 A1 ´ A2 ´ A3 2 P1A2 ´ A3 0 A12 P1A2 ¨ A3 0 A1 2 P1A2 0 A1 2 P1B 0 A2?

c. If the next customer lls the tank, what is the probability that regular gas is requested? Extra gas? Premium gas?

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Modern Mathematical Statistics With Applications

ISBN: 9780534404734

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Authors: Jay L Devore

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Question Posted: Sep 10, 2024 12:02 PM

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