Question

A switch-over event in a producing well occasionally results in a reportable oil leak. An analysis of the data shows that the chance of a reportable leak is 1 in 500 switch-over events. It is observed that 10 switch-over events occur every day. If the occurrence of a reportable leak follows a Poisson distribution, the number of days in a year (of 365 days) with no reportable oil leaks from switch-over events is ............. (rounded to nearest integer).

Hint:

For Poisson processes, the expected count of “no events” is obtained by multiplying the zero-probability $e^{-\lambda}$ with the total number of trials (days).

Answer 1

- Probability of a leak per switch-over event = $\dfrac{1}{500}$.
- Number of switch-over events per day = $10$.
- Expected number of leaks per day ($\lambda$) = $10 \times \dfrac{1}{500} = 0.02$.
- Since leaks follow a Poisson distribution, the probability of zero leaks in a day is: \[ P(0) = e^{-\lambda} = e^{-0.02} \approx 0.9802 \] - Expected number of days (out of 365) with zero leaks: \[ 365 \times 0.9802 \approx 357.8 \; \text{days} \] - Rounding to the nearest integer gives 358 days. (Some solutions may approximate as 357).