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A certain roller coaster has 3 cars, and a passenger is [#permalink]
30 Aug 2007, 02:39

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?

Each time the passanger rides he has a 1/3 probability to ride each cart.
to ride in each cart after 3 rides he must ride in carts 1-2-3 or 1-3-2 or 2-1-3 or 2-3-1 or 3-1-2 or 3-2-1
favorable outcomes = 6 (3! he should ride each cart once so first time he has 3 choices, than 2, than 1)
possible outcomes 3*3*3=27 (meaning he can choose each of the 3 carts each time he rides)
so 6/27 = 3/9 = 1/3
Answer D
what is the OA?

Re: Roller Coaster [#permalink]
30 Aug 2007, 03:21

solidcolor 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

I got B.

3 times 3 = 9 total possible outcomes. Among them only one is favourable. As long as the outcomes are 'equally likely' the result must be 1/9

Re: Roller Coaster [#permalink]
30 Aug 2007, 03:49

solidcolor 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

Actually, considering order in which the roller coaster rides the cars is important, that is what agps did; the total # of possible outcomes is 24, and the # of favourbale outcomes is 3...but there is no among answer choices 1/8

# of favourable outcomes = 3*2*1=6
(In the first round, the passenger has 3 cars to choose from, in the second round he has just 2 and in the third round he has just 1 if the passenger has to sit in all 3 cars by the time he finishes 3 rounds)

# of favourable outcomes = 3*2*1=6 (In the first round, the passenger has 3 cars to choose from, in the second round he has just 2 and in the third round he has just 1 if the passenger has to sit in all 3 cars by the time he finishes 3 rounds)

# of favourable outcomes = 3*2*1=6 (In the first round, the passenger has 3 cars to choose from, in the second round he has just 2 and in the third round he has just 1 if the passenger has to sit in all 3 cars by the time he finishes 3 rounds)

Probability=6/27 = 2/9

You've got it.

I have another explanation.

The first round, he can choose any car out of the three, 3 choices among 3 cars, P(1) = 3/3 = 1.
The second round, he has only 2 choices among the 3 cars, avoiding the car he took in the first round. P(2) = 2/3
The third round, he has only 1 choice left, avoiding the other 2 cars that he took in the first two rounds. P(3) = 1/3

Probability for "and" + "and + "and" should be
P = P(1) * P(2) * P(3)
= 1 * 2/3 * 1/3
= 2/9