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probability

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by finance » Mon Aug 08, 2011 6:54 am
A certain roller caster has 3 cars and a passenger is equally likely to ride in any one of the 3 cars each time he decides to ride. If a passenger is to ride the roller caster 3 times, what is the probability that the passenger rides in each of the 3 cars?

- 0
- 1/9
- 2/9
- 1/3
- 1
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by Frankenstein » Mon Aug 08, 2011 7:03 am
Hi,
Let the 3 cars be a,b,c
In each of his 3 turns he can choose any of the 3 cars.
So, total possibilities = 3*3*3 = 27
Now, for him to choose different cars in each of his turns, he needs to select a,b,c in any order. This can be done in 3! = 6 ways
So, probability is 6/27 = 2/9

Hence, C
Cheers!

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by gmatboost » Mon Aug 08, 2011 7:47 am
Another approach is:

First time, he can go in any car.

Second time, he can go in either of the cars he has not been in yet: [spoiler]Probability = 2/3[/spoiler]

Third time, he can go in only the one car he has not been in yet: [spoiler]Probability = 1/3[/spoiler]

Answer: [spoiler]2/3 * 1/3 = 2/9[/spoiler]
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