Results 1 to 6 of 6

Math Help - Help me, please

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    20

    Help me, please

    Would you help me with this problem?

    3 out of 4 trucks are followed by a car, while only 1 out of 5 cars are followed by a truck.
    What fractions of vehicles on the road are trucks?

    Thank you in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by maria_stoeva View Post
    Would you help me with this problem?

    3 out of 4 trucks are followed by a car, while only 1 out of 5 cars are followed by a truck.
    What fractions of vehicles on the road are trucks?

    Thank you in advance!
    Pr(T | C) = 3/4.
    Pr(C | T) = 1/5.

    Using a Markov chain and letting n --> oo I get 4/9.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301
    Quote Originally Posted by mr fantastic View Post
    Pr(T | C) = 3/4.
    Pr(C | T) = 1/5.

    Using a Markov chain and letting n --> oo I get 4/9.
    What do these probabilities represent? The probability that you have a truck given that it is followed by a car?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2009
    Posts
    64
    Quote Originally Posted by Sampras View Post
    What do these probabilities represent? The probability that you have a truck given that it is followed by a car?
    Each vehicle in the line is a state of the markov chain.

    So, as stated in the problem, the probability of going from 'state truck' to 'state car' is 3/4 and the probability of going from 'state car' to 'state truck' is 1/5.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2008
    Posts
    20
    How do you get 4/9? I don't see that
    Thank you!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by maria_stoeva View Post
    How do you get 4/9? I don't see that
    Thank you!
    One way is to examine the limit of T^n as n --> oo, where T is the transition matrix (in practice, just raise T to a large number like n = 30 and deduce the limit).

    Alternatively, an approach using eigenvalues can be used.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum