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Need help with number of equiprobable outcomes

  • #1

Homework Statement



A subway train made up of [itex]n[/itex] cars is boarded by [itex]r[/itex] passengers [itex](r < n)[/itex],
each entering a car completely at random. What is the probability of the
passengers all ending up in different cars?

Homework Equations



[itex]P(A) = \frac{N(A)}{N}[/itex]

[itex]A[/itex] - no more than one passenger enters any car

The Attempt at a Solution



Part 1. Finding the total number of equiprobable outcomes [itex]N[/itex]
The book says that the number of equiprobable outcomes [itex]N[/itex] is [itex]n^r[/itex].
I've set up a table (included in the attachment) with 3 cars and 2
passengers and came up with only 6 equiprobable outcomes. What
I don't understand is that the passenger will not be in two cars at
once so why would the solution be [itex]N = n*n*...*n = n^r[/itex].

EDIT:
Another book with the same problem with the same solution.
 

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Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Homework Statement



A subway train made up of [itex]n[/itex] cars is boarded by [itex]r[/itex] passengers [itex](r < n)[/itex],
each entering a car completely at random. What is the probability of the
passengers all ending up in different cars?

Homework Equations



[itex]P(A) = \frac{N(A)}{N}[/itex]

[itex]A[/itex] - no more than one passenger enters any car

The Attempt at a Solution



Part 1. Finding the total number of equiprobable outcomes [itex]N[/itex]
The book says that the number of equiprobable outcomes [itex]N[/itex] is [itex]n^r[/itex].
I've set up a table (included in the attachment) with 3 cars and 2
passengers and came up with only 6 equiprobable outcomes. What
I don't understand is that the passenger will not be in two cars at
once so why would the solution be [itex]N = n*n*...*n = n^r[/itex].

EDIT:
Another book with the same problem with the same solution.
The 6 you have there is the number of restricted outcomes where there aren't two passengers in any car N(A). The N in the problem is the number of total outcomes, where any number of passengers can be in a car. The N is 3^2=9. which is the n^r. The probablity is the quotient. Got it? The N isn't the restricted outcomes. N(A) is the restricted outcomes.
 
Last edited:
  • #3
Oh yeah. That's very stupid of me. :redface: Thanks Dick.
 

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