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Interesting question about car driver

  1. Sep 20, 2005 #1
    Hello, I tried to model and answer this question, but I didn't get success. Could someone help me ?

    Question:

    A California driver decides that he must switch lanes every minute to get ahead. If he is on 4-lane divided highway and does this at random, what is the probability that he is back on his original lane after 4 minutes (assuming no collision) ? [HINT: the answer depends on whether he starts on an outside or inside lane.]
     
  2. jcsd
  3. Sep 21, 2005 #2

    AKG

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  4. Sep 21, 2005 #3
    If the driver is outside at the far left , you have these possibilities

    R,R,R,L
    R,R,L,L
    R,R,L,R
    R,L,R,L
    R,L,R,R

    R IS MOVING RIGHT , L IS MOVING LEFT

    He returns to his lane when the number of R equals the number of L

    p= 2/5

    When the driver on the second lane from left , we have these possibilities

    L,R,L,R
    L,R,R,L
    L,R,R,R
    R,L,L,R
    R,L,R,L
    R,L,R,R
    R,R,L,R
    R,R,L,L

    WHEN #R=#L, He returns to his original position

    p = 5/8
     
  5. Sep 21, 2005 #4
    How reach the right answer ?

    ------------------------------
    This question is in a book, that giving the answers.

    The right answers are:
    from an outside lane: 3/8;
    from an inside lane: 11/16.
     
    Last edited: Sep 21, 2005
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