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Poisson Process Probability Question

  1. Mar 1, 2014 #1
    Hello,

    I have this one problem but have no idea how to get started.

    Avg. number of accidents is .4 accidents / day (Poisson Process)

    What is the probability that the time from now to the next accident will be more than 3 days?

    What is the probability that the the time from now to the 3rd accident will be more than 5 days?

    Any information / formulas would be appreciated.
     
  2. jcsd
  3. Mar 1, 2014 #2
    The trick to finding the probability of a given event is to express it in terms of probabilities you know. For example, [itex]\begin{eqnarray*}
    P(\text{next accident is the day after tomorrow or later}) &=& P(\text{no accident today or tomorrow}) \\
    &=& P(\text{no accident today}) \cdot P(\text{no accident tomorrow}|\text{no accident today}) \\
    &=& P(\text{no accident today}) \cdot P(\text{no accident tomorrow}) \\
    &=& P(\text{no accident on a given day})^2 \\
    &=& [1- P(\text{accident on a given day})]^2
    \end{eqnarray*}[/itex]
     
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