Most financial institutions compute a daily risk measure for every portfolio of a set of instruments that is of interest to them, called the daily VaR (Value at Risk) of that portfolio. This VaR value is a dollar amount, generally obtained through a statistical model, such that the probability that the next day's loss in the portfolio will exceed the VaR value is a small pre-determined probability. So, for example, a 1% daily VaR value of, say 5.2 million $, means that the model says that P(tomorrow's loss for the portfolio > 5.2 million $)=1%.

The two most common probability values used in practice are 1% and 5% and the corresponding VaR value is called the 99% VaR and the 95% VaR, respectively. The daily

VaR value changes from day to day, as the volatility in the underlying market for the portfolio changes and the model tries to account for the change.

The VaR value plays many important roles, one of which is to set capital requirements for the financial institution. To check whether a particular VaR model is working adequately, the Basel Committee, which is an international quasi-regulatory body, outlined the following backtesting rule:

For each day over a period of 250 days (which is approximately the number of business days in a year), the institution has to compare the actual loss for the day to the 99% VaR number (note that the 99% VaR number is such that the probability of the loss exceeding that number on a day is 0.01). The institution is declared to be in a "green" zone if the total number of days that the actual loss exceeded the 99% VaR number over the 250 days is at most 4.

Assume that the VaR model is working well (i.e. that the actual probability of exceeding the VaR number on a day is indeed 0.01). What is the probability that the institution will fall in the "green" zone?