17. At a certain gas station 40% of the customers request regular gas, 35% request unleaded...

17. At a certain gas station 40% of the customers request regular gas, 35% request unleaded gas, and 25% request premium gas. Of those customers requesting regular gas, only 30% fill their tanks all the way up, while the remaining 70% only fill up part of their tank. Of those customers requesting unleaded gas, 60% fill their tanks all the way up, while of those requesting premium, 50% fill their tanks all the way up. If the next customer does not fill the tank all the way up (only fills it up part of the way), what is the probability that they requested regular gas?

	a.	0.120
	b.	0.280
	c.	0.514
	d.	0.545
	e.	0.264

Solutions

Expert Solution

P(regular gas / does not fill way up) = P(regular gas and does not fill way up) / P(does not fill way up)

P(regular gas and does not fill way up) = 0.40 * 0.70 = 0.28

P(does not fill way up) = 0.40 * 0.70 + 0.35 * 0.40 + 0.25 * 0.50 = 0.545

P(regular gas / does not fill way up) = 0.28 / 0.545 = 0.514

ANS : Option C : 0.514

orchestra answered 1 year ago

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