High School

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As a transportation and logistics coordinator for company "x," you are responsible for making vehicle rental reservations for all incoming business partners. Next week, 3 partners are flying into town, and you need to get vehicles rented for them. There are currently 21 SUVs and 6 sedans available. If you make 3 reservations where the vehicle type is selected at random, what is the expected number of sedans that will be reserved?

Answer :

Final answer:

The expected number of sedans to be reserved when making 3 random reservations from a pool of 21 SUVs and 6 sedans is 2.

Explanation:

The student is asking about the expected number of sedans that will be reserved given a random selection process from a pool of 21 SUVs and 6 sedans, with 3 reservations being made. To calculate the expected number of sedans, we can use the concept of mathematical expectation.

Since there are a total of 27 vehicles (21 SUVs + 6 sedans), the probability of selecting a sedan for one reservation is 6/27. Because there are three independent reservations, we can multiply the probability of selecting a sedan by the number of reservations:

Expected number of sedans = probability of selecting a sedan times number of reservations

Expected number of sedans = (6/27) times 3

To calculate:

Expected number of sedans = 2/3 times 3

= 2

Therefore, the expected number of sedans to be reserved is 2.

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