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Probability

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by pakaskwa » Thu Apr 02, 2009 12:10 am
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

My answer is not even in the list. Can someone help me?
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by DanaJ » Thu Apr 02, 2009 12:21 am
First time he rides the roller coaster the probability of him picking a cart he hasn't ridden before is 1, since it's the first time he rides it.
Second time he rides the roller coaster the probability of him picking a cart he hasn't ridden before is 2/3, since he's already ridden one of the three carts.
Third time he rides the roller coaster the probability of him picking a cart he hasn't ridden before is 1/3, since he's already ridden two of the carts.

So my answer will be 1*1/3*2/3 =2/9.
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by pakaskwa » Thu Apr 02, 2009 12:55 am
Thanks Dana. It makes sense.

I had difficulty because I translated the problem: there are 3 balls in a bag, each in different color. Pick up any one ball from the bag without looking into it, then put it back. What is the probability of picking 3 times and each time it's a different color?

I think it's the same as the original question (taking different car each time for 3 times). So my calculation is 1x1/3x1/3=1/9. What is the problem in my calculation or translation?
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