# Poisson Process Probability Question

1. Mar 1, 2014

### sakebu

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. Mar 1, 2014

### economicsnerd

The trick to finding the probability of a given event is to express it in terms of probabilities you know. For example, $\begin{eqnarray*} P(\text{next accident is the day after tomorrow or later}) &=& P(\text{no accident today or tomorrow}) \\ &=& P(\text{no accident today}) \cdot P(\text{no accident tomorrow}|\text{no accident today}) \\ &=& P(\text{no accident today}) \cdot P(\text{no accident tomorrow}) \\ &=& P(\text{no accident on a given day})^2 \\ &=& [1- P(\text{accident on a given day})]^2 \end{eqnarray*}$

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