Question

Given that the car has not failed in the first 4 independent trails,what is the probability that it will first fail on the 7th trial?

It is known the car will fail one tie in the 100 trials

Answer 1

The car fails in 1 of 100 trials.

So, the chance that the car fails is 0.01 and the chance that the car does not fail, is 0.99.

We have to find the chance that the car first fails on the 7th trial, given that it does not fail in the first 4 independent trials.

Now, probability of not failing, ie. passing the first four trials is

Now, Probability of failing first on the 7th trial, and passing all the first 4 trials means passing the first 6 and then failing the 7th trial.

This can happen with chance

So, we have to find

By conditional probability definition, this is

So, the answe is 0.009801.