Question

the bargain Auto Mall has the following cars in stock

	SUV	Compact	Mid-sized
Foreign	20	50	20
Domestic	65	100	45

If a car is selected at random, find the probability that:

1. The selected car is compact.
2. The selected car is compact and domestic.
3. The selected is compact given that it is domestic.
4. The selected car is compact or domestic.

Answer 1

All the below questions are simple probabilistic problems which can be solved by just counting the number of favorable outcomes to total outcomes possible.

Now total number of cars is the sum of

20

50

20

65

100

45

which is simply equal to 300.

a.

P(Car Selected is Compact)

= Total number of compact cars / Total number of cars

= (50 + 150) / 300

= 1/2

b.

P(Car selected is compact and domestic)

= 100/300

= 1/3

c. P(Selected car is compact/Domestic)

= P(Selected car is compact and also Domestic) / P(Selected car is domestic)

=

=

= 10 /21

d. P(Selected car is compact or Domestic)

= P(Selected car is compact) + P(selected car is domestic) - P(Selected car is compact and domestic)

= 150/300 + 210/300 - 100/300

= 260 / 300

= 0.8667

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