Thread: Binomial probabilities with a twist..

1. Binomial probabilities with a twist..

Hi everyone,

I have a hard time with a probability question, can someone help?

Assume there are n identical banks. Each bank has a probability of 0.5 to go bankrupt after one time period.

If presumably more than x banks go bankrupt, all banks are saved by the government. Obviously, x < n.

I have all my money at one bank. What is the probability of it going bankrupt?

Does anyone have an answer? Guess it has something to do with the cumulative binomail distribution in order to calculate the probability that banks actually go bankrupt... or is it?

Cheers,
T

2. Originally Posted by instantaneous
Hi everyone,

I have a hard time with a probability question, can someone help?

Assume there are n identical banks. Each bank has a probability of 0.5 to go bankrupt after one time period.

If presumably more than x banks go bankrupt, all banks are saved by the government. Obviously, x < n.

I have all my money at one bank. What is the probability of it going bankrupt?

Does anyone have an answer? Guess it has something to do with the cumulative binomail distribution in order to calculate the probability that banks actually go bankrupt... or is it?

Cheers,
T
The probability of any particular bank going bankrupt is given to be 0.5. I doubt your particular bank is an exception to that. So the proability will be 0.5.

Unless of course it's to be assumed that government intervention means that banks that would have been bankrupt are no longer bankrupt. In which case the probability will be 0.5 - Pr(x < number of banks that go bankrupt < n). I will let you consult your class notes or textbook on how to calculate the second term.

(Ahhh banks. You've got to love them .... Privatise profit, socialise risk).

3. Originally Posted by mr fantastic
The probability of any particular bank going bankrupt is given to be 0.5. I doubt your particular bank is an exception to that. So the proability will be 0.5.

Unless of course it's to be assumed that government intervention means that banks that would have been bankrupt are no longer bankrupt. In which case the probability will be 0.5 - Pr(x < number of banks that go bankrupt < n). I will let you consult your class notes or textbook on how to calculate the second term.
Because we already have our bank bust we need to subtract the probability that x-1 or more of the remaining n-1 banks go bust.

CB