Fed fund futures are actively traded instruments on the Chicago Board of Trade. The contract is cash settled to the simple average of the daily effective Fed funds rate for the delivery month. Although the daily effective Fed funds rate is not perfectly equal to the Fed funds target rate, it is very close. Market practitioners use the Fed fund futures rate to gauge the markets assessment that the Fed will change the Fed funds rate. Suppose that there will be an FOMC meeting 10 days into the current month. Use the following variables, if t as the Fed fund futures rate, i _{pre t} as the target rate prevailing before the FOMC meeting, i _post t as the target rate expected to prevail after the FOMC meeting, p as the probability of a target rate change, d₁ as the number of days between previous month end and the FOMC meeting, d₂ as the number of days between the FOMC meeting at the current month end, and B as the number of days in the month.

(a) Write down a general formula for the probability of an FOMC target-rate change.

(b) Given that the current target rate is 3.5%, the expected rate after the meeting is 3.75%, the Fed futures implied rate is 3.60%, there are 30 days in the month, and the FOMC meeting will take place on the tenth day of the month, what is the probability implied by the market prices that the Federal Reserve will raise interest rates?