# Nuclear Probability Question

## Homework Statement

The frequency of a tsunami large enough to threaten the safety of a nuclear power plant has been estimated to be 1 in 200 years. If the plant’s life is 65 years what is the probability it will be damaged by such a tsunami? What is this probability more commonly termed?
[2 Marks]

## Homework Equations

How do you get a base event failure rate for components with no recorded failures in an operating time T? Let λ = k/T. A Pessimistic Failure Rate λ = 1/T is known as ‘one tomorrow’. A PSA could use k = 0.5525 (For the estimation of failure rates for low probability events see Progress in Nuclear Energy 4 374-476 1997).

## The Attempt at a Solution

Probability of no damage = e-λT

λ = 0.5525/200

Probability of damage = 1-e-(0.5525/200)(60) = 0.153

A pessimistic failure rate λ=1/T is known as 'one tomorrow'.

Is this correct or completely wrong? Thank you

mfb
Mentor
How do you get a base event failure rate for components with no recorded failures in an operating time T? Let λ = k/T. A Pessimistic Failure Rate λ = 1/T is known as ‘one tomorrow’. A PSA could use k = 0.5525 (For the estimation of failure rates for low probability events see Progress in Nuclear Energy 4 374-476 1997).
You are overthinking this. The problem statement gives you the rate. Where this number comes from is a different question not relevant here.

You are overthinking this. The problem statement gives you the rate. Where this number comes from is a different question not relevant here.

Are you sure? So would you say 0.325? Seems too simple.

mfb
Mentor
You'll still need the exponential function.

You'll still need the exponential function.

Do you get 0.259?

λ = 1/200
Probability of damage = 1-e-(1/200)(60) = 0.259

mfb
Mentor
That's how I would answer the problem.