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A certain roller coaster has 3 cars, and a passenger is

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A certain roller coaster has 3 cars, and a passenger is [#permalink] New post 07 Aug 2007, 13:09
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A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the
3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride
the roller coaster 3 times, what is the probability that the passenger will ride in each of
the 3 cars?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1
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Re: DS...Roller Coaster [#permalink] New post 07 Aug 2007, 13:59
smily_buddy wrote:
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the
3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride
the roller coaster 3 times, what is the probability that the passenger will ride in each of
the 3 cars?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1


Probab to ride in any of the cars: 1/3.

Cars: A, B, C.

Number of possible rides: number of combinations of A, B, C where no letter (car) is repeated = 3! = 6.

Total number of possible rides = 3x3x3 = 27.

Probab = 6/27.
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Re: DS...Roller Coaster [#permalink] New post 07 Aug 2007, 14:13
smily_buddy wrote:
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the
3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride
the roller coaster 3 times, what is the probability that the passenger will ride in each of
the 3 cars?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1


C.
First pick is any
Second pick is 2/3
Third pick is 1/3
2/3 * 1/3 = 2/9.
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 [#permalink] New post 07 Aug 2007, 16:19
Great the OA is C...
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 [#permalink] New post 07 Aug 2007, 18:24
First time -> choice of any 3 cars
second time -> choice of any 2 cars
Third time -> choice of 1 car

Total number of ways for passenger to ride in each of 3 cars = 6
Total number of ways a passenger can ride (over 3 rounds) = 27

P = 6/27 = 2/9
  [#permalink] 07 Aug 2007, 18:24
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